2 weeks in Germany/Austria...time management help!

Yes, its a tuffy, only 1 night in Prague, preceded by 2 nights in Berlin, one of which will be jet lag recovery.
Its an age old problem, you want to do a 3 week trip but you only have 2 weeks vacation. Can you see if you can get it to 16 nights?

We did not see a night/sleeper train available from Berlin to Prague

Correct. German Railways (DB) has discontinued most of the night trains. There is a regular express train every two hours from Berlin to Prague (about 4.5 hours ride).

If you want to save time, you may consider a flight (approx. USD 180): https://www.kayak.com/flights/

Seems doable, but is it too impossible?

You try to squeeze a four weeks' endeavour into 14 days. I presume you are greatly underestimating your jet lag, the travel times to and from your hotels, and between the different locations. You can't really do several sights in one day. You need time to rest, to eat and drink, and to give your brain the chance to digest what you have seen.

I have found that I could almost always stay longer somewhere to see more/experience it better. You need to decide if you would like to do a "surface" visit of every place you mention, or take things a little slower and see fewer places but get a deeper experience in those places. If it were me, I would stay longer in Berlin (an amazing city with such a wonderful vibe) and cut out Prague and Vienna this trip, but that's me. Whatever you decide, relax and enjoy!

Two nights in Berlin really isn't worth much of anything. The city has many sights, a lot of them are large/time-consuming, and stuff is spread out so considerable time is spent just moving from sight to sight. I'd urge you to skip the city and hit it on another trip, but you seem to be flying into Berlin, so I guess that's not a good suggestion.

One night in Prague means just a few hours once you get there. So my reaction, again, is: Why bother going? All that time spent checking in and out of hotels, transiting train stations, sitting on trains... You don't see more with this kind of schedule; you see less, because you lose so much of your time to relocating.

Also, starting off a hectic trip with a 2-night stop, a night train and a one-night stop is a good way to be totally exhausted before the mid-point of your trip.

You've simply got too many destinations there.

thank you all for the tips! Think we will cut out Prague if there is a night train to/from Vienna...any chances of that? The 2017 guidebook of Vienna, Salzburg & Tirol states there are. We could reverse the plan of our trip and end in Berlin if there is that as an option.

Yes there is a night train from Berlin to Vienna taking 12 hours. Leave at 7 pm and arrive at 7 am. I just looked at a couple of August midweek departures, and there do not seem to be any savings fares available. 2 people in an Economy sleeping compartment is 318 EUR and in a Deluxe compartment is 358 EUR. The train makes several stops throughout the night. Think about a airplane flight.

Yes there is a night train from Berlin to Vienna taking 12 hours. Leave at 7 pm and arrive at 7 am. I just looked at a couple of August midweek departures, and there do not seem to be any savings fares available.

Not quite correct. There is a Sparschiene-Nightjet bargain fare for €29, but that is for a seat, only, i.e. no sleeper.

For about the same price you can go by Flixbus (9.5 hours ride), but this is a daytime connection.

The cheapest flight I found ( https://www.kayak.com/flights/ ) was a $48 bargain fare, regular fare is $88 and up.

I think that you haven't done yourself any favors by flying into Berlin and out of Frankfurt if your intentions are to visit Prague, Vienna, Salzburg and Munich. You are wasting precious time by moving around so much. The distances between all of these locations should not be underestimated and flying might be better for many journeys.

My suggestion would be to focus on Berlin, Nuremberg, Dresden, Rhine and Frankfurt. Otherwise, fly immediately to Vienna and spend the bulk of your time in Vienna, Salzburg and Munich.

Your are self-described "laid back" folks, but what you are proposing is not relaxed at all.