Hi Tom, lets try to answer some of your questions. Firstly, sorry to hear about your illness, I hope it doesn't interfere with your playing too much.
I find that my embouchure weakens very quickly. If I don't play at least once a week I start to loose strength and it takes a little while to regain it. I wouldn't let it worry you too much, you can cheat slightly, drop a reed strength for a week or two until you've strengthened up the old gob a bit.
Now then, as for the busking, first of all contact the council
here's their website they should be able to tell you if you need a licence and if they allow buskers in the town so that covers the legality side of it.
As for amount of tunes, how many do you know? Are you able to just play along with backing track to a tune you know or will you need the music in front of you. I don't read music so that answers that question for me, and, apart from that, I don't think it looks good if you've got a stand in front of you.
As for the backing tracks, you'll need something to play them on. This is my prototype
Empybuskbox, it was very simple to make and cost me about £15 it's easy to carry about (I put it on a small trolley) and I simply play my mp3 backing tracks straight through it. I don't use a mic, in the streets you don't need one. The acoustics on the streets are normally great!
I would suggest that you pick about ten tunes. If your fingers aren't that quick and you don't do fast intricate fingering then I'd pick some nice slow ballads, Wonderful world, Summertime, What a difference a day makes, Fly me to the moon, these always seem to go down well and are enjoyable to play. You can really concentrate on your tone while you play them.
If you know and like these tunes I can send you the mp3 backings if you want. Just PM me your email and I'll get them to you.
No doubt some of the others will have something valuable to add, but I hope this gives you something to go on.