I'm doing what you are doing: performing a nominally research-oriented job in industry and publishing on the side. This and this earlier answer of mine may be helpful. To your questions:

1. You should discuss whether you should put your employer's name down as an affiliation. My employer allows this, even on work I do that is utterly non-related to my day job.

2. You being in industry should not matter. Hopefully. This will depend on your field - in one of my fields (forecasting), it may be a slight plus, in the other one (inferential statistics for psychology), nobody cares, because I'm only one of five co-authors, and never the lead author.

3. No idea about this.

I'm afraid that industry research positions on theoretical computer science will be extremely rare. Good luck finding and getting one of those!

If you can't get something in theoretical CS, you essentially have two options - either switch fields to something more applied (in which case you will need to both learn the basics of this field and establish a new reputation and network), or continue your theoretical CS work in the evenings. In this case, your employer will likely not pay for you to attend conferences, so you will either have to pay yourself and take vacation time to go, or forego the networking opportunities conferences offer. In addition, I have found that I'm too tired once my kids are in bed to do any scientific work, and I hate spending the time they are awake writing non-work related papers - my kids don't see enough of me as it is. Your mileage may vary.

I'm doing what you are doing: performing a nominally research-oriented job in industry and publishing on the side. This and this earlier answer of mine may be helpful. To your questions:

1. You should discuss whether you should put your employer's name down as an affiliation. My employer allows this, even on work I do that is utterly non-related to my day job.

2. You being in industry should not matter. Hopefully. This will depend on your field - in one of my fields (forecasting), it may be a slight plus, in the other one (inferential statistics for psychology), nobody cares, because I'm only one of five co-authors, and never the lead author.

3. No idea about this.

I'm afraid that industry research positions on theoretical computer science will be extremely rare. Good luck finding and getting one of those!

If you can't get something in theoretical CS, you essentially have two options - either switch fields to something more applied (in which case you will need to both learn the basics of this field and establish a new reputation and network), or continue your theoretical CS work in the evenings. In this case, your employer will likely not pay for you to attend conferences, so you will either have to pay yourself and take vacation time to go, or forego the networking opportunities conferences offer. In addition, I have found that I'm too tired once my kids are in bed to do any scientific work, and I hate spending the time they are awake writing non-work related papers - my kids don't see enough of me as it is. Your mileage may vary.