It seems, you are doing something wrong. First, "peasant" garrison available right from the start, in first after-tutorial mission. (You still need to build it, of course). Also, you would pick a lot of contracts from lairs and dungeons, if you are working with it. Theoretically speaking, if one border province give you problems - put hero here and start to search for troubles/treasures.
So you will get money, fame, items, experience, and guard province simultaneously!
Also, I believe, there is some "disable animation" option hidden somewhere.
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Checked. It's during battle. You can select speed, "quick" and "auto" battles, if you find it too slow.