You use the basic rotation on everything, slightly modified for the particular content you are running. As mentioned, lower hp mobs you don't need to put dots (CT/Phleb) as they will die before you get the full effect. It doesn't seem to be there on the new dragoon thread, it's on an obscure post somewhere but you can duplicate the math yourself:

If an enemy will live 10 sec you have at least 4 attacks

HT TT VT FT

If 5 attacks

HT ID TT VT FT

6 attacks

HT ID Dis TT VT FT

etc etc, just add the potency up and see which attacks will offer the most damage

Regarding fates, you can still execute the full rotation from the front (in the past if you didn't hit the positional it would break your combo so you literally could not do half your rotation, but they changed this back in second coil) if you think the mob will live long enough (or if you're solo'ing the fate).

It really depends on the encounter but you should try to use the full rotation anytime possible if for no other reason to build muscle memory and familiarity with various techniques.