First Europe Trip

Welcome to Thorn Tree. Just a few comments - firstly, of course you are in northern Europe at the end of winter. Be prepared for snow, frosts, etc. particularly in Germany and Czech Rep. Not really the weather for camping anywhere in Feb / March You'd need to go quite a long way south for warmer weather - Italy, Spain, southern France.
Next, start thinking in Pound sterling and euros. At present I think you are talking of around £3000 or 4000 euros. - all the web sites you are likely to check will be in these currencies. It depends on what you expect this to cover (everything - accommodation, food, travel, entrance fees, an occasional beer???). Does it include air fare? Are you intending to get an open jaw ticket (fly into one city - London? - and return to US from another - Prague or wherever you end up).
Hitching is no longer common in Europe. You might to check the german site mitfahrgelegenheit which is a sort of car share arrangement mainly within Germany. German railways website bahn.de has times for trains throughout Europe though it is worth checking the individual train sites of each country for deals on fares.
Assuming your airfare is in addition to your 4000 euros, then say 250 euro per week for food and basic accommodation should be adequate. You'll really need to check out trains fares admission fees etc, but my guess is that you should perhaps assume another 150 euro per week minimum. That means a max of 10 weeks, depending on how far you travel, perhaps 8 weeks with a safety margin.
Hope you get some advice from others on here, and when you've got your itinerary a bit clearer post something on the Western Europe site for extra tips.

You might to check the german site mitfahrgelegenheit which is a sort of car share arrangement mainly within Germany.

There are versions of this for most countries in Europe. Germany is the most common. But you can swing rides for cheaply and its always fun meeting a few locals/fellow travellers as well. You basically chip in for Petrol. I caught a ride from Ljubljana to Munchen last September and it cost me 25 euros. I saved 15 euros if I was to take a bus there and I saved about 50-60 euros on a train. It was a far more enjoyable and pleasant experience. Check it out.

Considering you have about 3-4000 euros for a month and a half that is plenty. Especially in the 'low' season. But you won't be meeting a heap of fellow travellers. You may be the only one in some hostels. Hit up Couchsurfing.org to meet locals (they can always show you around, grab a coffee/beer at a a great cafe/bar and what to see). Its also invaluable if you want to save moolah on accomodation. Eating is fairly inexpensive if you just want to stick to eating from the supermarket.

I've been doing research into a trip to parts of Europe, regulars can give you more info if this is of interest to you but places like Croatia, Bulgaria, Romania, Serbia etc might be warm enough for winter camping by mid-end Feb and have awesome bush walking/sights. Why I suggest them is they are much cheaper than Northern Europe countries like Germany, Netherlands etc and could stretch your budget out longer.

Depends if the goal is to be on holidays for longer, or specifically experience the countries you have listed above?

You do understand that the snow doesn't melt in Prague until April don't you? Camping is not going to be happening at that time of the year - I would imagine 99% of the camp grounds will be closed as well.

Sacah, even in those Balkan/Med countries, it gets rather chilly. Madrid/Istanbul/Sofia can all get snow. So I doubt you would want to camp there. And as midlifetravel said, most will be closed. Some will be open for caravans etc but you'd be crazy to camp.

I did a quick search of temperatures in a few places in Croatia end of Feb this year before posting, temperature was same as winter in Sydney and the camp sites here are still open and have crazy people camping in them, my wife meet up with a couchsurfing lady from Czech who was camping in a tent this winter in Sydney, it was even raining at the time. Maybe the few places I picked were low lying warmer places as none listed snow.

Not my idea of a good time, but she loved it.

My post was mainly to see if the poster was interested in modifying his plans to extent his holiday, if so the regulars could better advise of times and cheaper places to camp.

Average temperatures would be about that. But it still snows in those regions. I would skip the whole camping idea as a whole. Especially at that time of the year. The OP has enough money (if that 4K doesn't include his airfare) to last and be able to go for that amount of time. Hostels will be cheap at that time of the year too.

Morocco and Egypt are pretty cheap (compared to Western Europe) but the problem is getting there.

You can take a ferry to Morocco, but Egypt is much father and you can't get between the two overland; there's no open border between Morocco and Algeria and there's a war going on in Libya

I'd stick to one region and explore it thoroughly.

Good luck.

You can take a ferry to Morocco. Whilst certainly true, you still need to get to Spain to take that ferry. Better to just fly there. Same with Egypt.

I'd stick to one region and explore it thoroughly. Best advice. Follow this as always. You have a decent amount of time but focus on a smaller area (say Bavaria/Czech Republic) and you will have a much better time than trying to fit in Morocco and Egypt.