Moderators can both change and lock trust levels of users (see screenshot here in the discourse moderation guide). This happens through trust level 4 users (“Leader”) cannot do this. As far as I’m aware the list of trust level 4 abilities in the article is pretty exhaustive (of course, you additionally also have to look at abilities listed for lower trust levels).
Trust level 3 (“Regular”) will automatically be taken away again, once the numbers go back below the threshold.
If you read the article carefully, you’ll see it actually containing the answer to these last two questions:
All of the above criteria must be true to achieve trust level 3. Furthermore, unlike other trust levels, you can lose trust level 3 status. If you dip below these requirements in the last 100 days, you will be demoted back to Member. However, in order to avoid constant promotion/demotion situations, there is a 2-week grace period immediately after gaining Trust Level 3 during which you will not be demoted.