Derelict doesn't like anal. That's why.
The snake lady is now in the desert area, and you can't activate the portals until you reach her (unless you use the imma lazy sack cheat).
To unlock new areas blocked off by the Cockblock Gates, you have to talk to blessed nephs. They are the unique ones, with names and a unique look. Each one has a specific request for you, for a certain type of neph. Fulfill their request and they'll give you their keystone, which can be used to open a gate. Keystones are generic, any keystone works on any gate.
The breeding requests board has a Special Requests tab which lets you see the blessed requests once you've gotten them. That's also how you complete the quest. Then go to the blessed neph to get the keystone.
Don't steal the keystone from the slime unless you want to make her cry (sad ending for her). Progress further on and there's something (I think a pearl?) that you'll find that you can give to the slime for her keystone (happy ending for her).
The game is meant to be very lewd, yes. That is the entire point of the game. Derelict is very focused on making the game as erotic as possible, though he does have some caveats about what counts as erotic.