1) We have many Discounters, per example "Hofer", "Penny Markt" or Lidl. For dishes or furniture only IKEA comes to my mind, but there are other shops (like LEINER or KIKA) that have some good offerings throughout the year.
2) The best supermarket is "Zielpunkt" IMO, it´s not that big as SPAR or BILLA but i think the bread and the meat is better than at the others.
3) If you buy a Student-Semester Ticket for the public transport you don´t need to pay for every single way. It costs you 100 € per semester (1: October till January, 2: March till June) and for February you need to buy a month ticket, which costs 30 €. The public transport is very well organized and also very safe, don´t worry
4) IMO the public transport is that good organized, that you don´t need to have a bike - but in Vienna there are a lot of parks, so maybe you want to go on a ride at the weekend. Then i would recommend you one
5) Well, of curse you need to see the "Ring", there are the most beautiful buildings of Vienna next to each other. Then you have to see of course the Stephansdom, the Kärtner Straße and so on. There are many things to see in Vienna
In the evening you will have tons of possibilities to have fun
If you have any other questions, you can PM me or ask in this thread. As soon as it´s possible i will answer you