Your comforts in a hatchback.
Hi and Welcome to the Great American Roadtrip Forum.
If you stick to campgrounds with an attendant and truck stops, you should be safe. But have you considered other potential obstacles? For instance, where will you put all your possessions when getting ready to sleep, and getting dressed, not just when you are sleeping. You can't stand up in your car, and depending on which hatchback it is, you may not be able to sit up on the mattress.
So when are you planning on doing this? There are other comforts to consider depending on the season, which will affect your comfort, and hence your trip. In summer a hatchback can get unbearably hot, and in winter there is condensation to prevent. You can't keep the engine running. You'd end up being poisoned. Neither would you want to sleep with the windows open.
Covering all the windows is a big red flag. Whereas I know you would do it for privacy, as would I, but it is a message to others that you are sleeping in there. Not such an issue so long as there are others around who know you are in the vehicle. Have you considered getting a small tent, sleeping bag and mat?
I would be wary parking overnight when you are the only one in the campground. Also, be sure to always tell reception at the truck stop of your overnight plans. Let them know you are there, and make sure it is OK with them.
Stay safe.
Lifey
Some Hints from Experience
Similar to rcquinn, I did a lot of sleeping in my car when I was younger. It helped that my first car, though small, was designed to make up into a bed. I later did minor modifications (mostly changing out the bolts on the passenger seat back so that it would fold all the way forward to the windshield) that allowed me to do pretty much what you are planning to do with my next two RoadTrip vehicles, a 1972 AMC Gremlin and a 1979 Subaru Outback, that turned them into quite serviceable sleeping platforms. Note that everyone of those cars was a hatchback, more or less. The key is to find the length to stretch out at full length and as nearly horizontal a possible. If you have to sit or curl up this really doesn't work.
As far as curtaining things off, I wouldn't. As noted, it would just advertise that someone's sleeping inside. If safety is a concern, there are other ways to address it. One, make sure someone knows that you're there. This is easy enough if you're parking in a truck plaza. They're quite used to such things. Just let them know your plans and make a point of buying something from them, a meal, a cup of coffee, a shower, whatever. Second, be ready to make some noise. This could be as simple as being ready to hit your car horn, putting your key fob (if it has a 'panic button') on a wristband while you sleep, or getting a small airhorn or whistle. In either case, you're actually going to want to keep at least a couple of your windows rolled down about half an inch or so to get some ventilation while you sleep. If noise and light bother you, get some ear plugs and a sleep mask.
And finally plan on spending every third night or so in a motel with a real bed/shower/TV to just relax and fully recharge.
AZBuck
Not leaving yourself much choice.
Most of the big truck stop have laundromat facilities. Free camping places rarely have any more than a basic toilet - which you would not want to use to get changed in. State Parks/Forest campground these days average between $15 and $20 - depending very much which area you will be travelling in, which you have not told us. But counting on $10/night seems quite unrealistic. You'd end up spending the two in between night at truck stops, which may or may not be plentiful in the area.
Do note though that not all truck stops welcome overnighters..... not even all FJs. I know in States like Illinois and Indiana there are some 3 dozen Pilot/Flying J of which about 7 welcome RVs and folk sleeping overnight. You might like to get hold of this directory, which lists the relevant truck stop. Flying J also put out a small booklet which shows where RVs/overnighters are welcome, and some of their other services.
If you want to stay at hostels, I suggest that you check out this site for hostels in the area where you are. By booking directly with the hostel (or just turning up) you can save yourself around $3, which is the fee the booking service charges the hostels.
Again, depending on where and when you will be travelling, all these facilities and prices differ.
Lifey