Nobody has yet used the balloon analogy - excellent (bleedin terrible analogy and a lot to answer for).
I normally start with the piece of elastic analogy when trying to explain expansion and the lack of centre. Pull elastic and your fingers move apart. They are not moving relative to the elastic so each can claim, justifiably, to be stationary. From that POV the other finger is rushing away at increasing speed (and in fact the speed is proportional to the distance - the further away, the faster it recedes).
There is a basic analogy for expansion.
When it comes to inflation - many physicists don't really much like it, it has the feeling of a convenient patch, but it does work and you don't ditch a theory because of it's origin - you test it and try your very best to refute it - that's science.
On GR - we know that GR is wrong, but it is so right for most things that, rather like Newtonian mechanics, it is a very useful and used model. If we can ever get QED/QCD and Relativity together for long enough in the same room without one of them sulking and dividing itself by zero until it feels better, then we will know a bit more. If we ever find the damn elusive Higgs then a bit more still, and if we start seeing micro black holes at the LHC then (and only then) I'll dust-off some string theory texts and start swatting.