Gretchen's last name is Schwartz, not Black. Schwartz is German for "black", but she wouldn't sign her name G.B.
Also the inscription in "Leaves of Grass" was almost exactly the same as the one in Gale's Lab Notes book.
Gale didn't necessarily give him the book on the first meeting. I guess I should have clarified it wasn't the next scene, it was the next scene with Walt. There is a scene between with Hank watching Jesse's house, and he's been there an indefinite amount of time. Marie calls and asks "are you ever coming home?" and there's a few days worth of fast food wrappers on the seat next to him.
So yeah it's still kinda
that Gale gave him the book after only knowing him a few days but Gale was a weirdo that idolized Walt. He was on Walt's dikk before he even met him, when he was discussing the 99.1% purity in Season 4, Ep 1. When Walt told him he'd rather work with Jesse in Season 3, Ep 8 Gale acts heart broken.
Lastly, Mike was watching Jesse's house, the same way Tyrus was watching the DEA/Hank's house/Gus's house. He tells Jesse "this guy has been at your house for 3 days". He had to have been watching the house to know that.