[Does buying and getting Fiverr Learn badges will increase gig ranking?]

No, It Doesn't. Courses are only certification

[Gig impressions down how to improve?]

You can increase your gig impressions and clicks by doing SEO of your gig. SEO of gig means targeting the low competition niche and adding those keywords in gig title and gig tags that people are actually searching on Fiverr. Include thode keywords in gig description as well.

[Why is my account currently under review by Trust and Safety team]

It means exactly what it says: you made gigs that violate the terms of service on Fiverr. It refers to the services you offer in your gigs. The team will now evaluate what to do next, and there's nothing you can do but wait for their action.