Newbie questions about becoming an integrator, how to get into robotics field.

Well, you definitely want to take at least the basic Operating and Maintenance training courses for whatever brand of robot you want to specialize in. Beyond that, there are lots of specialized courses for unique applications that you can wait to take until you need a particular one.
Getting a "beater" used robot to practice on in your own shop would be a good idea. You can also use it to test end effectors, try out processes, etc. As you've already read, you need to be careful about buying used robots, but careful selection can get you a cheap robot that's generally "okay" without trapping you with a machine that's not supported and can't get spare parts for. For ABBs, a retired IRC5 from an auto plant might be a little too beat up for production work, but should still be okay for non-production use, and should still be well-supported by ABB. An S4C+, on the other hand, I'd be more cautious about.

Formal education can be good to have, but isn't vital -- a lot of integrators do fine with learn-by-doing. I have an electrical engineering degree, which doesn't really apply directly to my day job, but in my lab courses I learned a lot of troubleshooting skills which do apply directly.
The manufacturers generally don't care -- if you can pay for their training course, they'll accept you. As far as being "certified" by them as an integrator, you get a certification for each training course you take. If you want a more formal relationship with them, that's usually a business-to-business relationship.

There are lots of integrators that don't have any sort of "official" certificate. I certainly don't, although I have certs for various training courses I've taken over the years. Some integrator companies have formal partnerships with ABB/Fanuc/etc, but many don't. As far as getting a "general integrator" cert from one of the Big Five, I think you'd have to ask each of them individually.
In my experience, most small inexperienced customers don't know anything about integrator certifications, and don't care -- they just want someone who knows what they're doing. You're probably going to be starting at that end of the market, and establishing a word-of-mouth reputation to begin with.

If you want to build a business model around buying used robots and selling them as part of integrated systems, that can work, but you have to be really careful about long-term service and support from the manufacturer. Because when the customer's robot breaks, they're going to call you, not ABB. Establishing a relationship with a reputable dealer who refurbs and resells used robots will be important -- there are more than a few cheap-out artists operating in that space. If your refurber can also provide repairs and tech support for the robots you buy from them, even better.

I've worked as an employee of several automation integrators over the past two decades, and used all of the Big five (KUKA, Fanuc, ABB, Kawasaki, Nachi) during that time. But over time, I moved into areas (mainly aerospace production) where KUKA dominated. So while I can "get by" to various degrees on the other brands, my most advanced work has mostly been done on KUKAs. Also my most painful learning experiences. So it's where I have the most to offer (and most often have need of assistance).

Generally, the Big Five will sell to anyone. Where they can get "tight lipped" is when you start digging into things that aren't documented, or are internal-only information, or just exotic information only known by a few top-level people in the company. At that level, it helps a lot to have a professional relationship with the manufacturer, or to have someone on the inside you can call to get past the regular help-desk people. OTOH, for 90% of general industrial applications, this isn't a problem that arises. It really helps to do careful research in advance, however -- I've had cases where someone bought a robot with (for example) EtherNet/IP installed, brought me in to integrate it to their existing systems, and don't understand when I explain to them that the EIP robot can't talk directly to their existing ProfiNet network (without adding new hardware and setup costs). "But it's all Ethernet, why doesn't it Just Work?" So, avoiding situations like that can help you avoid situations where you need an "inside person" at the manufacturer.

As you build a reputation, building a relationship with the manufacturer, or with your local supplier for that manufacturer, will get easier, and building this relationship is important. But it takes time. You can start out as a "basic level" integrator without this relationship (and every new startup has to), but nurturing it is something that should always be part of your ongoing routine.

The reason to take the classes is mainly for your own benefit -- there's plenty of "tribal knowledge" that doesn't come through the written documentation. It can also be your first "contact" inside the manufacturer -- if you show up and ask intelligent questions, and show you really want to dig into these robots and do creative things with them, rather than just be a button-pusher for Automobile Manufacturer XYZ, most instructors like that and might be more amenable to teaching you some off-the-books details, and maybe even let you call them in the future for some quick technical advice.

Cheap-out artists aren't necessarily scammers. But while they may well sell you a robot that works, it probably has been stripped of everything, including the Install disks, wiring diagrams, etc, beyond an utter bare-bones machine. There are some that will buy a used robot, power it up and jog it for one minute to confirm it "works," then sell it to you with no documentation or support whatsoever -- that's how some people in the KUKA forum end up stuck with old VW-version KRC1s that it's nearly impossible to find parts, manuals, or even know-how about. So it's really a matter of doing your due diligence. If the reseller can't provide history for this robot, or what versions/options it has installed, or the backup media or wring diagrams, proceed with extreme caution. A good reseller will be able to support the machine, and will provide some of those items, or at least be able to tell you where to obtain them.

I worked for ABB for a few years then worked at a small systems integrator mainly using ABB robots in welding applications. I found having an industrial electrical background helpful when designing/building the controls side of the installation while other did the engineering design and fabrication. We had no accreditation, just the skills and ability to build and install machines to customer requirements, although in EU countries you will normally need to meet CE marking requirements.
You say ABB have a big market share where you are, is there a particular application they are used for?, welding, handling etc., so it may be worth specialising in one of those areas.
The ABB programming course would be a good investment to get you started and as stated by SkyeFire buying a used robot to practice on and improve your skills is a good idea.
Global Robots Ltd are a well known supplier of good quality used robots with good back up.
Hope this helps.

Possibly relevant: https://www.robotics.org/Become-A-Certified-Integrator.

It is certainly possible to work on robots without taking any of the training courses. But that generally requires some sort of on-the-job training. Or getting a "beater" robot and learning the hard way. Selling yourself as an integrator without any training or experience will be... risky.

On the downside, if you take all the ABB training courses, and then your potential customers all ask you to integrate Fanucs, you've just... well, not wasted your money, but invested it in the wrong brand at the wrong time.

One option might be to start with the low end of the market -- the UR robots are, I'm told, very easy to learn, and are certainly cheaper than any but the most beat-up beater "big" robots (also, can run off of normal wall-socket power, unlike most industrial robots). They seem much more amenable to a "teach yourself" approach, and you could treat them as an on-ramp to establishing yourself as a reputable integrator before taking the next step up to bigger, more expensive, more dangerous robots.

For the safety side of any machines you design/build, you need to look at risk assessments and what needs to be incorporated to mitigate the risks.

Not sure where you are, I am UK based and when I designed and built controls for robot/automated welding machines I had to document risk assessments, which along with a lot of other stuff went into the "technical construction file" as part of the process to get our machines CE marked.

It's probably been about 15 years since I did systems integration and I believe if you get all the paperwork correct you can apply the CE mark, there were about 3 approved companies who would go through the relevant paperwork and issue the CE mark (at a cost) if you did not do it yourself.
It's mainly a papertrail of materials,suppliers etc. for traceability, as if anything ever went wrong in the future, government bodies, courts etc. always want to blame someone