Cool! It’s interesting to observe your experimentation through your questions. As you will find, tags are powerful and can be used in many ways, but the tag management UI is a bit confusing at times.
As regards (1) In my experience, it has been fine to be loose with tags when letting users add them. You just have to carefully garden them on a regular basis so that no tags remain in “Other tags” but are all categorized or deleted. You and your moderators can also help ensure that topics are tagged correctly. This is not that time consuming (depending on the size of your site of course) and is helpful for understanding how the site is being used. You can then use a topic in site feedback to guide your members as to how you want them to use tags.
With (2) you could use a category template to prompt users to provide the information in a structured way in the topic at least and also to add tags if they are up for it. If not you and your moderators can help make that happen.
With (3) you can limit tags or tag groups to multiple categories. Have you tried it?
If you are feeling ambitious, you can look at Custom Wizard Plugin 🧙 which provides you with the ability to create forms. But that can get complicated real fast!