The midgame is usually the stage of the game where the teamfights start. Of course teamfights are better played with 5 people than with 4 (although sometimes the toplaner isn't joining you during early midgame) which means that you should be around an objective together with your other teammates.
Now of course this isn't the only option. As you've pointed out correctly it highly depends on what situation you are currently in but over all your main goal should be securing kills to snoball into lategame. You are the guy that cleans up the enemy team after everyone is low since you usually have less damage than the mid or top laner. The more kills you get the stronger you'll be in your most important phase: The late game.
Obviously you still deal a nice amount of damage especially on objectives like dragon and turrets. Which is why you should try to safely bring damage to these without falling out of position.
Now to specifically answer your 3 questions:
We didn't take the bot turret
Well that's a pity but it's not that bad. The outer turrets are more or less uninteresting and can be done if you see that no teamfight is coming up. The outer turrets have low health and are often used to snowball. Just go down there to finish it off if you are sure that you won't be needed in a teamfight and if there are no enemies heading for you.
The other Team is grouping
Now here we have 2 options: if you are stronger than them - Group. If you are weaker - Rotate. If you are stronger you should obviously try to kill them. Stand behind your tank/supporter and try to finish off enemies after they've dropped low. If you're weaker take your support and start splitpushing and/or grab some jungle camps. You should also try to defeat them while defending a turret but make sure you don't get assassinated.
Losing/Winning
Well I mentioned it above but I'll say it like this again: If you are stronger than your enemies you should force fights and objectives like dragon. If you are weaker than the enemy team try to rotate and look out for an advantage.
Final word
ADCs are kind of irrelevant during midgame. All you have to do is getting fed for the lategame and help getting objectives. The most important thing is: Never go anywhere alone! Always take at least your supporter with you.. Usually you are squishy and horrible at 1v1s (well maybe not if you're Vayne or EZ).
