Your wife's visa will be tied to yours as a dependent. If your company can handle it for you and pay for it, I would let them.
Help with your taxes is key.
By real estate agent, do you mean a relocation agent? Real estate agents are called estate agents here and they are VERY neighborhood specific. Something more beneficial, would be to ask for a couple of weeks to a month or more of temporary housing while you search for a neighborhood you like and a place to live. As far as relocation agents, some people find them very helpful and some people find them annoying.
You say the job is long term but something else to consider is getting them to agree to repatriate you should things not work out or at the end of whatever
"long term" ends up being.
After a good clean out, we moved all our stuff over and they paid for it including a few months of storage in the US while we found a place to live. I have no idea how much it weighed but 5000 pounds sounds at least sounds like a lot.

We had 1 round trip per year paid for by the company.
I suggest ask for whatever you want, well don't go crazy, and they can only say no. I don't think anything in your list is unreasonable.
*ETA: I defer to ks on the visa stuff since things have changed a lot since my husband and I went through the process.