At 10 lev, you will receive a university contact for the recipe tutorial. Completing the tutorial awards the Inventor Badge. University - Unofficial Homecoming Wiki
Bladehook spawns like Winter Lord. After a number of Spectral Pirates from chests opened in zone, he will appear with a crew at next chest opened. ☠️ 🏴☠️
The extra costume slot missions are still available. Costumes - Unofficial Homecoming Wiki
The City Representative also offers cape and auras missions for heroes.
City Representative - Unofficial Homecoming Wiki
Mr. Rodney on offers cape and auras missions for villains.
Mr. Rodney - Paragon Wiki Archive
I'm surprised no one has directed you to JJ's builds yet. His builds are solid, but no/very little franken slotting. He is also still doing requests. Usually, my first go to search for builds.
When I can, I like use exploration Tip mission to find those badges. The mission flag takes you right to it. No wondering around until you find it ... left, right, up, down.