Likely the dog is either bored or a little anxious in the change of you moving in your boyfriend's house. First, keep the trash in a place where the dog cannot get to it. Give attention to the dog when you are there, take the dog out for more exercise.

Sounds like he's bored being alone. I would kennel him while you are not there to supervise.

separation anxiety

Could be because there was a major change in the dogs life or it could be separation anxiety. But what you could do is take your dogs food and mix canned with it. Then stuff that mixture into a kong and freeze the night before so its frozen when you leave. Give the dog the frozen kong and leave the house for 20-30 minutes, this way your dog will get used to you leaving with a yummy tasty treat. By the time they are done getting the frozen food out they should be tired.

If things were up where the dog could not get them, you wouldn't have problem. If you pick up & put up all the things he could destroy you will be dog proofing you home. If it is down & he gets it, your fault. Put things up out of sight. Don't leave things down that the dog could hurt himself on/with.

This could be separation anxiety or it could be just a dog bored out of his mind. Bored dog get destructive. You need to supply this dog with lots & lots of different CHEW toys & some 'interactive puzzles/toys', google that.

I think the dog needs more exercise, more training, more socialization.

I hate crate training & I will help you do away with the crate.

it couldnt if things were kept out of its reach eh

Dogs are opportunists and if you leave out things he can get into and he 'finds' something to eat or play with then that is self training/self praising.......... so it is up to you to never leave anything out he can get some 'food/toy' such as in your trash as clearly he has before, 'earned' the food ( self praise) so he will continue to go into the trash 'just in case' you left some more goodies for him to find and there is no use disaplining a dog AFTERWARDS when you get home and find the mess/stolen items as it is too late the dog doesn't associate the disapline with the action he did, he just associates getting disaplined because you arrive home and that will start to cause anxiety and that will cause chewing and peeing in the house ........so you need to disapline yourself, put away all and anything, empty the trash each and every time and leave him something he can chew like a raw bone or chew toy

He's bored and has energy to burn. Give him some exercise as often as possible

Boredom? How much daily exercise does the dog receive?

Also you cannot correct the behaviour unless you actually catch him in the act of getting "into" something as he will not understand what correction means.

You can only "prevent" the behaviour by making sure there is nothing he can get "into" when you leave him alone or by crating him.

Also taking him for a nice walk before leaving him may induce him to want to sleep rather than get up to mischief.

My answer is just all guesswork as I don`t know your dog or his daily routine.

This is quite simple .... he's upset at being left, for however long. I'm afraid if you can't confine him to somewhere he can't be destructive (for his own good as much as your's) he will have to be crated. Just don't leavel him in there for hours and hours. 4 hours is best practice, for an adult. His recent move, with you, might have upset him a bit too.

Separation anxiety... that's it.... google it.