On the issue of license plates, I will repeat what my old man drilled into me at a young age: "No plates are a misdemeanor (a ticket), and no insurance is a felony". His point was that no plates was not a big deal, but that you should have insurance. He was an old school NYPD detective who worked the Auto Squad. I guess not all cops (or states) play by the same rules, so on this you decide how you want to handle.
On the cost of a fill up, if the tank is bone dry it will take 50 gallons to fill, so you are looking at some $200 to fill it up. Expect around 10 mpg.
For the portable heaters. the 12v units will not do a **** thing. You would need to be drawing starting motor amperage to make a difference in that huge, drafty cab facing 50 mph air blowing past. For this trip, sit on an old Army blanket and drape another one over your legs. Gloves, a good coat and hat and you will be fine. And noise suppression earmuffs like the landscapers wear. For aftermarket hot water heaters, look into the hot rod marketplace as there are units available for a lot less $$ if you do not care about authenticity. These units all hang under the dash. Check summitracing.com or jegs.com.