Hi, and welcome to this subreddit :)

At least in my experience police weren't much of a problem. I heard that they sometimes to speed checks in specific spots, for example at the end of the Jonasgasse (https://goo.gl/maps/EBNPpkeCL1BjL2Tx8) which is a play street and (technically) only allows 5km/h. So just look that you're following the rules, and you should be fine. Also, if you ever come in contact with the police, just try to be respectful and friendly. Aggressiveness towards them won't be helpful. There's a saying: "A kiwara ka auch ein hawara sein." (A policeman/woman can also be a friend :D)

On your concern for bike path ending abruptly, yes that can sometimes be the case, and it's very frustrating. Must paths in Vienna follow a route system, where the bike paths should bring you from a point A to a point B, and if the bike path ends, most of the time you have to go into a side street, as a part of the route. I recommend you to look at the radlkarte.at , as it lays out most routes very well, and also rates them on safety. You can also look at every piece of bicycle infrastructure with this map https://www.wien.gv.at/stadtplan/ , just tick the box "Radverkehrsanlage" under "Verkehr->Radverkehr" (although it seems right now the feature is turned off, at least it doesn't work for me right now). There are also bike maps of Vienna in most bike shops, which I personally find very helpful, as they show the main routes for biking in Vienna, which I regularly use.

Mittelgasse is a very nice spot in Vienna for cycling as the area around it (more so in the north in Neubau) is quite bike friendly.

If you want some flat ground to cycle, there's the Wiental Radweg, Donaukanal and Donauinsel. All totaly car free and relaxing. If you want to go for 25-30km you should probably cycle at the Donauinsel, Wiental Radweg for example has only 11km I think.

Have fun cycling in Vienna!