Yes, feed it, especially if the weather's bad.

Hopefully your own cats won't have any problems with the feral(?) cat. If they do, you may need to discourage it as your garden should be your cats territory & this could lead to more problems. Also beware if it's a 'full' tom-cat, smelly, territorial etc.

As to touching it, if it is 'wild' or 'feral' it may take a long time for it to trust you enough. I've persevered with 2 very feral cats over the years. The first one took me 6 months before it would let me touch him.

If it's really living on the streets it may get into all sorts of trouble & could turn up on your doorstep obviously needing a Vet's treatment. That's a good reason to gain it's trust & get to the point where you can touch it. If you can eventually get it to a Vet, then a full check-up is worth doing, with necessary jabs & possibly the 'snip' too.

This all sounds expensive, but is something to think about at the start of your friendship. Lots to think about.

Of course, it could be a 'lost' cat & someone is missing it terribly??