I've bivvied at Red tarn a few times with various numbers of my sproglets and pet dogs - and there are a few places around Red Tarn where you could put up a tent - and also quite a few alongside the beck just to the East.
The only thing is, its a very popular spot, - as darksky says, people wild camp there often so don't necessarily expect to be alone - and there's potentially a problem with human waste, particularly amongst the boulder fields.
As for Striding Edge - all I can say is that its not specially difficult in dry conditions but can be a bit disconcerting at first. Again, its a very popular route, so there's likely to be others having wobblies too, if that helps. Personally, if I'm going to throw a wobbler, I like to do it in private, unless I'm actually going to fall off, in which case a few witnesses can be handy...