1. Junction box/cover plate and the 30A rv receptacle (TT-30R?)
Yes. That is the correct female plug, assuming that your trailer has the equal male plug on the power cable.
2. 10 gauge electric wire
NEC states 10ga for a 30A circuit in this application. 10/2 romex for the run between the circuit breaker panel and the location of your trailer recept.
8ga could be substituted for the 10 on a longer run; this depends on the location of the main or sub panel that you are getting the power from.
3. 30A breaker? What kind/type?
30A single-pole breaker that is equivalent to the rest of the breakers being used in the panel. You may or may not be able to get a breaker type off of the face, and will need to pull the dead-front off to see what type of breaker you will need for your distribution panel. You may (should) find a sticker on the panel that lists the acceptable breaker manufacturer and model.
4. and a 100ft 30A rv extension cable?
Can I use the cheaper house electric cable rated for 30A and just the adpater?
Technically you shouldn't, but you can.
Romex is not rated to be outside, and must be protected. The proper 30A extension cable from Wal-Mart, or if you get a good deal on some 10ga or larger S.O. or other armored cable, you can make your own.
The last time I checked (a little over a year ago), it was cheaper to buy the molded cable from Wal-Mart than what I could by the cable and equivalent plugs for!
