You wouldn't need to shred the palm branches, but it would certainly help them break down much faster.

From the sounds of it, you have mostly high carbon sources, so you'll need to add some sources that have more nitrogen to get it to compost in a decent amount of time (it'll decompose eventually, but it'll happen faster with more nitrogen).

If your neighbors bag their grass clippings (since you come here, you probably mulch mow), you can ask them for their clippings and add them to the compost. Another source of nitrogen is coffee grounds. Starbucks has a corporate policy of giving them away for free. If there's no Starbucks nearby, you can probably talk to other coffee shops, restaurants, gas stations, convenience stores, etc to see if they'll save their grounds for you.

You will need to shred the palm branches. The darn things would make good bomb shelters, I swear. Used to garden under many many fan palms and date palms in California. They never ever break down on their own and I wouldn't even try them in my little leaf shredder, I was afraid they'd break it. You'd want a tree chipper for them. They make great roofing materials, I've watched guys in Mexico making palm thatch roofs.

As I understand termite biology, any wood material in contact with soil will attract them, so yes to the wood chips in the compost. Now if you keep your compost pile turned daily and hot enough that should keep the termites out. But, then the termites can get into the compost used as mulch in the garden, but I would think that once the wood is thoroughly broken down the termites don't want it anymore.

I have a bunch of large palm trees in my yard and I compost only part of them. I trim the leaves from the stems with clippers and then use a lawn mower to shred the leaves until they look about like grass clippings. These decompose quickly then. Unfortunately, I don't have a way to shred the stems, so those go to the dump.

I may see if I can shred the palm branches. If not, I might just use the method batdorf described. As for wood mulch, I found out that using wooden mulch will void our termite warranty, so maybe I will give up on composting anything wooden unless I can get a tumbler or some other sealed system. Thanks.