Hello! I did a little bit of freelance work but I'm really not a super experienced, so keep in mind that everything I say may not be all accurate.
1) I don't think it's necessary to mention it. Your client will only care about if you can deliver the work they need on time. The other things that you do in your life is not really something that they're interested in.
2) I'm not completely sure if I get what you mean here, but I'd say no. As I said, your client don't care if you work a part time job, so adding your schedule is unecessary. As for your income, just imagine your freelance job as being another regular job. The income you would do in one job will have no effect on the income of your second one, so the same applies here. You shouldn't be paid less just because you also work at another place.
All you'll need to do is making yourself a schedule to make sure you can meet your deadlines. But that schedule is not something you have to share. Depending on the jobs, you may have to work entire days on short notice and other times maybe just a few hours spread over a long period will be necessary. All that matters at the end is your ability to deliver.
I hope this helps, and as I said my experience is limited, but that's how it's been for me. Good luck to you!