Electric hook-ups depend on the site you are staying on. On busy sites, they often only have 6amp (that's the lowest I have ever seen) as they are sharing it between so many units, but 10amps is fairly common on the smaller sites. 13 to 16 amps is sometimes available on the small 5 van sites, but again, because of the price of electricity, many of them now limit it to 10amp, to keep spending under control. For some reason, campers do not seem to care about other peoples electric bill, and you have 5 caravans, all drawing their 16amps all night, thats £120 electric bill, and they often only charge £6-10 per night for it.
We were on a site a few years ago, that opened at Easter, and they gave everyone the full 16amp. This had not been a problem for many years, but this particular Easter, we had had a beautiful spell of hot weather up to the weekend, getting loads of people to go away, then on the Saturday night, the temp just dropped away, and fell to below freezing. Everyone went back to their units, and turned on the heating, which resulted in a fantastic fireworks display from the electricity boards pole mounted transformer in the corner of the field. There was no electricity for several days, and some electrician got into a lot of trouble for signing off the site. Now we only have 6amps per pitch, and not all pitches have hookup. Now the problem is, people blow the trips so often, that they go weak, and often trip at only 4 amps.
A lot of sites will not allow Tents to have hook up for the safety concerns, and cars tend to come under tents when camping, if they allow them at all, so you will be put in the corner for tents, well away from the electric hook up.
On a practical level, the car's fan tends to be power hungry, often around 10amps, so you would need to include a battery charger in your car as well, as the engine heater. The battery charger would need to be one that can output about 10amps, to be able to keep the battery topped up, so you then need to add another amp or so, to your 13amps the 3Kw engine heater draws. Lastly, my engine heater only lifts the engine temp to luke warm after an hour of running, but does not heat the car in any way. When you turn the ignition on, you see the temp needle just lift off the stop, but it does not even get onto the marks of the dial, and definitely would not keep you warm all night.