Immigration can of course check anything they want so there is a possibility. But I'm not aware of anyone being checked on entry, those applying for an extension in country definitely need to have signed up for a further activity
That is so specific nobody here can answer your question. What you or his doctor consider to be a disability may not match what the Thai authorities consider a disability and even if it does they may still refuse to issue one. You really are going to be much easier getting a Thai Privilege visa in that situation
Note that I believe the only way you can switch to a Non-B visa is to apply to do a conversion at an immigration office inside Thailand so make sure the company will supply the correct information to support that. Many companies want people to apply for a Non-B outside Thailand but you won't be able to do that unless you can find a way to first cancel your DTV (which won't be easy).
I guess you didn't have a printout of your evisa as you should have. I doubt you would have had an issue if you presented that along with your passport
No problem really. Every entry right up until the validity date gets you stamped in for 60 days so as long as your final entry is before that you're good