How odd RE: controller. Can't say I have experienced anything like that on either PS4 (across 4 controllers).
Strike wise you can tell what strike it is by the voiceover as you are flying in.
For example:
"Taniks has no house, he kneels to no banner" - This will be the Taniks strike (forgot the actual name of it).
When running strikes from the strike playlist they are in essence randomised (although you will often jump between the same strikes a few times during the process).
The level 36 and 41 (Heroic) strike playlist do no include all of the strikes available (for some daft reason). A lot of the "Year 1" strikes you will have played getting up to level 40 have not been brought forward. Devil's Lair, Summoning Pits and The Nexus are all missing. Given that every mission in the game has a light 240 "Heroic" option there is no reason why all of the strikes couldn't be in at least the level 36 list.