How hard is it to go from Salzburg to Hallstatt to Mink to Vienna? What is a recommended means of transportation preferable without renting a car.
Presumably you mean Melk, and all those places are easily reached by train.
Here's the Austrian rail company:
https://www.oebb.at/en/
Travelling is easy and mostly straightforward. But given the travel distances, you cannot do Hallstatt and Melk in one day. You can visit Hallstatt as a day trip from Salzburg, then on the next day leaving Salzburg early in the mornig to go to Melk, and continue your trip in the late afternoon to Vienna.
There are two routes from Salzburg to Hallstatt:
1: Salzburg to Attnang-Puchheim (express train), Attnang-Puchheim to Hallstatt (local train).
2: Salzburg to Bad Ischl (bus #150), Bad Ischl to Hallstatt (local train).
The travel time is about the same for both options. Option 2 is more scenic than option 1. If you choose option 2 and have enough time, I recommend a short visit of Bad Ischl. Walk to the famous "Zauner" café and pastry store and buy the unique "Zauner-Stollen".
The ferry from Hallstatt train station to Hallstatt town runs according to the arrival/departure times of all trains.