1) Short Rests in my campaign are an hour, and I generally limit them to "two per Long Rest". There is a Battlemaster/Rogue, Cleric, Rogue, Bard, and Warlock (celestial) in the group. During a short rest, the Rogue usually is scouting, the Bard is playing music, the Battlemaster and Warlock are regaining powers, and the Cleric... well, the player is usually not paying attention.
2) Warlocks are "magic-based martials". They are not Wizards/Sorcs. The 5th level Warlock doing 2d10+8 with a cantrip over and over is an output not matched by the Wizard or Sorcerer. The two spell slots are (in my mind) "just in case", not the focus of the class's abilities. The Warlock in my game (5th level now) has used Fly and Shatter; the one in the game where I play uses Form of Dread, and then Cure Wounds right before we rest.
On the other hand, I play a Sorcerer in that party with a Warlock. In the story we're playing right now, I conserve my magic a lot, frequently hitting a Long Rest with some magic remaining. We tend to have a "minion fight" and then a "boss fight"... but I'm always worried about the unexpected "wandering boss", so I hoard my spell points. On the other hand, during the last dungeon crawl adventure, we were always getting overwhelmed, either by aura/mass-attack bosses (spellcasting drider, electric crab-golem) or hordes of foes (gibbering guards, invisible duergar, dozens of cultists backed up by casters, etc.). I blew through my magic like there was no tomorrow... and ended up dragging along behind the group with just cantrips after they Short Rested. The dungeon was too dangerous for an 8-hour pause, and we were 4-levels down so just leaving them to scheme while we retreated wasn't a good option either. The Warlock did fine.
3) If one PC is taking a Short Rest and the others are busy doing things - like exploring, talking to NPCs, shopping, and maybe getting into fights - the player whose character is napping is getting left out. The other PCs might also - in character - get a little frustrated at their pal who is shirking. "Sorry guys, I can't scout... gotta 'commune with my Patron'!" or "You're going to go shopping? Can you pick up a dozen things for me? Sorry, I have to 'commune with my Patron'." If the majority of the group has Short Rest resources, though, then everyone takes that short rest... and the long-rest crew (if uninjured, like my Sorcerer usually is) are just twiddling their thumbs. I'm not about to go exploring by myself, so I just sit and wait for everyone to finish communing/exercising/bandaging. [I mean, my PC has an Addiction (Flaw), so he usually takes that time to "get mellow", but otherwise I have nothing to do.]