The boat does need to be registered, you will need to get that number from your charter company. Not everyone on board needs a license. I recent charter we had 8 people aboard, 3 had licences.
The boat does indeed need to be registered for fishing, and if you have the number that's great. In my case, my charter company (MarineMax) just told me to put "In Process" on the form. Whether they actually had started the process or not I don't know, but my application was accepted.
The hyperlinks for both forms are in my original post above...
Tom