Is there company sponsored housing?
No. You do get $3K/month (taxable) to offset miscellaneous costs of living on a remote island, which some people consider a housing allowance but it's usable however you choose.

What are the shipping arrangements for moving our belongings?
Company paid move to the island if you stay for 18 months, including shipping of 2 vehicles. If you stay less than 18 months (for reasons other than displacement), you pay a pro-rated cost of your move based on however early you leave. If you stay an additional 18 months, you get a paid move back. If you do not move within 200 miles of your new pilot base, the paid move back only gets your things to a West Coast port- NOT your new base. (I.e., transfer to ORD & move to ORD, company ships your things to ORD. Transfer to ORD & move to BNA, company ships your things to California.)

You also get 3K lbs/year of free shipping on UAL to use however you want.

Are there size and weight limitations?
Yes, for the company move, but it's pretty high. (Around 25K lbs.) I don't know of anyone who wasn't able to move all their home goods within that tolerance, but I suppose there's someone out there.