this depends on the cable, and also on the terminals you are using.
Would I get better results by using a hi-fi tape deck and an adapter so that both audio cables plug into the soundcard? (Does that adaper still allow stereo recording?)
Provided your tape deck has RCA connectors, I'd suggest using a cable with RCA connectors on one end and 3.5mm stereo plug at the other. Like this for example: http://www.reichelt.de/?ACTION=3;ARTICLE=30570;PROVID=2402
Is Audacity all I need or are there better programs?
Audacity is all you need. I strongly suggest to have a look at the tutorials on Audacity project website.
When playing a tape, does it matter about setting Dolby on or off?
This is something you need to try yourself. Sometimes the quality is better with Dolby "on", sometimes not.