I'm an AFOL (Adult Fan of Lego). Been one for over 10 years. I'm a founding member of our local group, see web page here: <http://www.nalug.org> (warning - slow site).
Yes, you can buy individual pieces online from Lego (look for "Pick-a-brick"). However, since there are now so many piece types and colours, only a small subset are available there. Also, they are expensive - Lego seems to sell by weight, so rare stuff is the same price as common stuff.
Yes, you can still buy boxes of just bricks, etc. without instructions. Again, however, Lego is expensive, and that's not going to change - the material itself is costly.
Competitors like Megabloks have now got their quality close to Lego's. One remaining issue is that because they use a different material (which is why they are a lot cheaper), they don't last as long - bits of it flake off when you connect the pieces.
The Friends sets seem popular here - there are rarely much of them in the stores. I haven't bought any myself, but I mainly buy sets for parts to build my own stuff. I'll repeat the mention of the "Creator" line of sets - very worthwhile - each shows 3 different projects for the parts, just like the old Technic sets did.
I don't like the new style of "lift arm" Technic sets, so don't buy them. I find them simply too hard on my fingers in this dry climate, especially for disassembly.