Let me preface this by song in definitely no expert having just recently added sheep to our property in November. They've been very East to care for up to this point though I'm sure there will be some challenges as with all animal husbandry. In doing my research on sheep I wanted to find a breed that would do well with my philosophy on life which is generally to let nature be our guide. This is how I approach beekeeping (which I'm also new at) and most things in life. Nature is wiser than I, I'm just here to try ronwork with nature.
All that to say... I determined an "unimproved" breed was likely better suited to this philosophy. They haven't been continually bred for show or certain looks, traits, etc and are largely the same as they were a few hundred to a thousand years ago. There were a few options such as Icelandic and Shetland to name a couple and I found a shepherdess with shetlands nearby so I settled on them. Both are nice looking breeds and smaller in size, which fits with my smaller homestead. Both were multi purpose useful for fiber and meat, the Icelandic is also considered useful for milk if desired.
In answer to your specific questions though. So far I have not sheared them though I will soon, likely after lambingnhas taken place although I'll probably dag the ewes before lambing to make it easier for the lambs to access the milk bags. I plan on using the better parts of the wool for making roving. Spinning, etc. The rough parts that aren't useful for that illnlikely add to my garden beds. They only need shearing once a year. As a point of interest you can roo Icelandic sheep, or gently pull tye fiber from them in the spring. They have a three part coat and partner it sheds.
So far they've been easy to care for, just providing clean water, hay, minerals, and shelter. They're pretty Hardy and don't care about snow or rain really spending time out in both.
Their temperament has been good, the ram is still young at less than a year and that may change as he gets older and shows dominance more. Another reason I picked shetlands is their smaller size. It hurts less getting rammed by a 100-110lb ram than a 200lb ram. Probably just bruises not broken bones. The ewes are a little standoffs but alhave been warming up to me, especially when I have grain. Aggression will be one thing I keep out of my gene pool as much as possible. If I have a ram that's being too cranky or aggressive I'll use him for dinner instead
Hopefullythat helps.