1.01 is the patched version, the one at launch was 1.0. As for how to get new patches, assuming you own the game on GOG and are not pirating it, the devs will release subsequent patches that will get added to your game in your library, in case you want to download them manually, or it will automatically update if you use GOG Galaxy.

[EDIT] As for that specific side quest, I, too, am playing with keyboard and mouse and didn't have much issue with it. I highly doubt watching a walkthrough will help you, since basically what you need to do is outrun the hounds that are awake and avoid the ones that are asleep. Then, when you enter the room with the Houndmaster, jump onto the cage on the left as Strife and just shoot him without killing any of the hounds he spawns. If you're having trouble with this particular extra goal, all I can say to you is "good luck later on", because... well... you'll need it.

Also, I don't know if this is helpful or not, you don't need to do side quests as soon as you go through a level, you can always come back later with a higher power level which makes doing these side missions A LOT easier (especially after unlocking your Chaos Form).