You can do a little bit of that with chesstempo if you have a premium membership. You just go to Problems - Problem search and make a set for each tactic type, but it won't have most of those categories. Also, the tags for the tactics are crowd-sourced and not super-reliable, so it won't be perfect even in that case.
You have hit on one of the major reasons that a curated tactics set prepared by humans is far superior to computer-selected sets with crowd-sourced tagging. Basically, what you want isn't really within the scope of chesstempo or any of these other internet tactics trainers.
Hello
I was studying tactics using Chess Tactics for Club Players and CT-ART which was great and improved my games a lot ,
Now am not using windows anymore and wondering how to use ChessTempo to make sets like what I have in CT-ART and Chess Tactics for Club Players , I want it by themes
Opening the d- and e-files
Opening the f-file
Opening the g-file
Opening the h-file
Opening files
Opening diagonals
Clearing ranks
Clearing diagonals
Clearing important squares
Clearing files
Decoying to pins
Decoying the king into a mating net
Decoying to attack lines
Decoying to Knight forks
Decoying to attacks by opening lines
Decoying to attacks by retreating pieces
Decoying to Queen forks
Distracting pieces from defending important lines
Distracting pieces from defending the back rank
Distracting pieces from defending other pieces
Distracting pawns
Distracting pieces from protecting important squares
Distracting pinning pieces
Intercepting a piece defending another piece
Intercepting a piece protecting from checkmate
Unblocking by decoy
Discovered attack
Using discovered attacks when attacking the King
X-ray
Mill