Hi Eddie!
I took this route or variations on it last summer during my double-crossing of Western and Eastern Europe.
We are now thinking of pushing on to Budapest which would mean 50 miles a day (pretty) fully loaded.
This is doable. Moreso if south- or eastbound. I pretty easily averaged about 70mi/day fully loaded, which meant also hauling 8+liters of water, as there was a heat wave in Romania and Serbia, and it spilled over to Hungary as well. Winds can be a problem if westbound. I got a bit tired by the 8th day of 30kph headwinds, but that's what drops are for.
Do you know if its possible to put bikes on the train back to Prague?
Yes, I found it possible. However, it can be hard to get to the station if your lodging is a bit away from the main station. The subways/metros all connect to the main station. There can be some elevators, but their clear a loaded Thorn Raven Tour by 3mm, so I foudn the escalator can be an option, though very steeply inclined. I stayed in Prague Sector 7 and my train left at 5:30am. Unfortunately, the metro line didn't operate that early, so I had to ride to the main station. On the freeway. In the traffic lane, as there were no shoulders. I was advised (and it proved true) it was the only way, so I left my hotel at 2:15am to make sure I would miss most traffic. I had to overshoot the station on the freeway 'cos and then circle back on the city streets to catch the freeway going the other direction to reach the station exit. Most platforms connect via underground passages, which means hauling a loaded touring bike up and down stairs, which is a good early-morning workout, as the stair interval does not match a touring bike's wheelbase. If you catch an older train, the entry will be up three or four *very* steep steps (high rise-to-run) with a sharp turn at the top, so it is best if you can remove the bags first. Best, but not always possible if doing this solo as I did. The bike hook in the bike car will have an assigned number to match your seat number, so it is important they match. Do be aware other cyclists are likely to use the trains in large numbers even in late summer, so getting a ticket for yourself and the bike does not guarantee a place for the bike on a particular train -- they can occasionally be oversold. Fortunately, the tickets are transferrable.
How strict is the "no wild camping" in this part of the world?
It can be lax...or very strict depending on location. Chances are much better in the countryside than in urban areas. Success is largely dependent on how stealthy one is. I am very good at stealth/wild camping, putting up within 3m of inhabited dwellings undetected, but it varies. I never cross fencelines and I never violate areas posted No Trespassing or Private Property. I would advise most folk to inquire at a store or dwelling to see if it is possible to gain permission to camp by setting up a tent in a side garden. People are nice, and chances are good. Anywhere along the Danube bike routes in Austria, there will be a wealth of lodging options, from pensions to private rooms to campings at reasonable rates; given this availability, wild camping there is strongly discouraged. There are vast areas along the river downstream from Vienna where it is possible to camp undetected, but it is not "allowed".
Prague is a very nice, picturebook tourist destination. Buy the "Prague Card" for discounts citywide. I did and found it to be a great value, as it included both a free guided water cruise and open-air bus tour and free or greatly discounted museum admission. I found it a real boon in Prague, but got by fine without the Budapest equivalent. Of the two, I preferred Budapest as it was a little quieter and seemed a more "classic" destination; I greatly enjoyed my visits there both ways.
You're in for a wonderful time, Eddie, and I wish you all the best -- wishing I was going again myself!
I hope this helps.
All the best,
Dan.