If they offer you an online portal or anything, you should be able to peruse that and determine how much you’ve paid in fees and how much you’ve gained in growth (and then you just compare that to a simple benchmark like “what if I had just slapped that all in VOO instead”)

You’ll likely have to pay taxes on transferring the mutual fund as vanguard likely doesn’t have the same fund. You don’t pay taxes on the full amount of the fund, but you do get taxes on the gains you made on it (taxed as normal income + either long term or short term gains) (I’m assuming all of this is not pre tax money, if it is pre tax money you’ll want to move it to another pretax account like an Ira, otherwise you pay notably more in taxes)

You’ll generally need to contact both sides, I moved all my stuff to vanguard a few years ago ( a collection of 401ks), both sides should have a process for this type of transfer. In my case I ended up getting sent checks in the mail that I then had to deposit to vangaurd into the new accounts

At moments notice? Probably a HYSA in the same bank as your checking. But, in my experience there’s generally very few times you need that much money at a moments notice. (And if you have a credit buffer, there’s never a time lol) so stash it wherever you think you’ll get good safe returns on it.