Trying to use eldritch blast on statues to see if they're monsters? Trying to re-charge encounters mid-encounter? Your initial post was correct - those people are ***(deleted for the sake of Eric's Grandma)*** and there's no point in playing with them unless you have to. If you have to play with them, tell them to shape up, or else start killing them off.
What's the problem? In the first case it's simply a matter of the DM knowing the rules and the problem is solved. You don't get your powers back after 1 round of resting IIRC. If a player says that he automatically kills a monster when he rolls a 20 or that he boosts to 1000 hit points by wishing for them out-loud, then the player is in error. Why lose sleep over it?
In the second case - who cares if the PC is blasting stuff right and left? First of all it's a dungeon. Secondly, why is it the player's fault if his character gets unlimited blasts?
Assume some sort of hypothetical "real-life" situation - what are some negative consequences of walking into hostile territory and blasting away and every object in sight? I'm sure you can add to this list:
(1) You make lots of noise and attract monsters
(2) The statue may contain a lever that opens a secret door, and now you've just destroyed it.
(3) The statue may contain, or be, treasure, and now you've just destroyed it
(4) The statue may be a petrified ally, and now he's had his head blown off
But these would be unusual occurances. It's just a statue. Now it's a statue with some scorch marks on it. Look bored and move on with the adventure. Or if it really bothers you, have your NPCs go to his house and fireball his statues. Whatever.
Also consider the fact that PCs in previous editions of the game could have simply set fire to the flammable parts of the dungeon with their torches. This is not completely strange behavior from hostile people in alien territory. You don't really expect them to sign the guest book and close the door on their way out, do you?
I would also consider applying some sort of fatigue rules to the Warlock in question. After all, if the fighter in the party wanted to bash up everything in the dungeon with his mace, then that's an approach I'd consider.
**
DM: "The tapestry in front of you speaks- 'I'm the Tapestry of Doom, to pass you must answer a riddle..."
Players: "We fireball the tapestry."
If this situation surprises anyone then it seems to me that they've been DMing for about a week. There's nothing wrong with that though, just chalk it up as a learning experience and make sure the tapestry is made of asbestos the next time. Expect smart players to solve problems.