A 12 days between vienna, prague and salzburg

Most of your questions are pretty basic. I'd suggest you start with a guidebook and think about what you both want out of your trip and start listing what appeals to you. There is a LOT of information on all your questions already posted here, so read the forums.
A few quick comments:

Re 2: Wachau is a region. Melk is a small city in the Wachau.
The Danube River runs thru the Wachau region.
Melk is a pretty town, with a very famous abbey.
The Wachau is famous for wine and for the scenic route along the Danube that strings together lovely villages and vineyards. The route can be driven, or done by bicycle. There is train service and river cruise ships as well for visiting the area.

Re 4: Probably not. Don't drive in Vienna. You need to look at the train and bus connections.

Re 6- There are no 'bad' neighborhoods in Vienna. It is more convenient to stay close to an U-bahn station. Note that the U6 line is least convenient for most of the tourist sites in the city. Search hotels in your price class and then check their address against the transit system. The Wiener Linien website is a good resource.

Re 5- Impossible to say from your post. You need to do some calculations about what you are interested in seeing and then compare the cost of tickets 'a la carte' vs buying a card.

Hope this helps.

3- Is it worthy to do a Daytrip from vienna to Budapest consedring its almost 6 hours distance ??!

Yes, because it is only 2:45 hours away from Vienna.
First direct train to Budapest departs at 6:39am.
Last direct train back to Vienna departs at 8:40pm.

So you can have a maximum stay in Budapest of about 11 hours.

Then back from salzburg to vienna to the airport !!

Make sure to take a train which goes from Salzburg directly to Vienna Airport.
There are 22 connections of this kind per day (first departure 6:05am [arrival 8:57am], last departure 7:12pm [arrival 10:27pm]).

Question 1: Cesky Krumlov is better to do overnight. First - it is 6 hours roundtrip just sitting on the bus. Second - when mobs of the day drive away you have that magic just of yourself. The same for Hallstatt although it's a little closer to Salzburg.
Question 2: Melk is a small town in Wachau valley through which Danube flows.
Question 3: roundtrip distance is somewhat shorter.
Question 4: no
Question 5: probably not
Question 6: stay in center, pension Nossek in Graben.

If you decide to do a day trip to Budapest, then I would skip the day trip to Bratislava. Bratislava is OK, but it's not all that impressive. Personally, I wouldn't plan anything less than 5 days in Vienna.

Re: Is it worth it with your time constraint? That depends. It's more worth it than going to the Wachau valley and Melk. I prefer the day trip to Budapest regardless of the almost six hours r/t much more than going to Melk. Spend the extra time in Vienna, skip Bratislava and Hallstatt

I disagree about skipping Hallstatt. I would spend a night there. You could also consider staying in Melk in between Vienna and Salzburg.

If you don't have the RS guidebooks for these areas I would suggest you invest in them.