Hi, debbie--Some responses!
1) Yes, you could use a pallet as your base, with the advantage that it would bring some air in underneath. However, that will make it a little harder to shovel/scoop in there as the pallet may get in the way when you are trying to dig compost out.
Typically I start my compost on bare ground, with some "rough stuff" like corn stalks or weed stalks at the bottom for a little air. Being in touch with the ground also makes it easy for worms to come and go. So there's no real rule to follow here, just various pros and cons of doing it either way.
2) pine needles--yes, you can put these in your compost, and yes, they are "brown" high-carbon matter just like leaves. Some people say they decompose slowly, but so do some types of leaves so I don't think that's a big issue. See this little article: http://www.finegardening.com/how-to/qa/pine-needles-compost.aspx
Pine needles as mulch--yes! They are great for this. Some people worry they are too 'acidic' for the garden but this is probably not an issue, as they will make only a tiny effect on your soil's pH once they decompose. The benefits are great and the worms will love it.
On the other hand, if you already have very acidic soil you might want to withhold the needle mulch--however I doubt if your soil is acidic, it's more likely the opposite in your location, just a guess. Ask around some of your neighbors or the county extension to see if they know what the pH is of the soil in your area.
3) I agree with Plumerias that chicken wire will work, but watch out for getting scratched. One way to avoid this is to get some scrap lumber (like 1x2's) and staple or nail the two open edges of the wire to the wood, so that instead of grabbing the wire to open it up you grab onto the wood. Her suggestion of using burlap to keep the pile from drying out is a good idea, however burlap will decompose relatively quickly so if you're going to purchase something I'd buy some landscape fabric instead. This breathes, but is designed to hold up at least for a few years.
4) Plain cooked veggies in compost--yes.
5) location--it really doesn't matter. Lots of pros and cons of where and how to locate it but I would just put it where it seems best to you. Next year you could always change the location again if you wish.
Clay soil--Plumarias gives great advice about planting 'green manure' like winter rye in the fall. I have used this technique and it really, really works. In addition to all the benefits she mentions, it also suppresses weeds very well. There is quite a bit of extra digging involved in turning over the soil in the spring, etc. but in a small garden this is very doable and it pays off.
The other thing about clay soil is that although people struggle with it and complain about it, actually clay soil tends to be quite rich in minerals. So if you can get it loose enough and add enough organic matter to fluff it up, you can grow really good crops in it.
I'm sure you will have some successes and some failures, just as we all do! I've been gardening for 25 years and I'm still always learning more, still succeeding in some cases and having dismal failures in other cases! That's the nature of gardening, always wondering how things will turn out!