Hi, I resucued my husky from a shelter 2 years ago, and he was the sweetest and friendliest dog. I moved recently to the country and got him 2.5 acres to play in. Unfortunately, he started digging under the fence and my neighbors been complaining about it. The area is full of stray dogs and other people dogs that roam around and get on my property too. Today I found a poor puppy dead in his mouth, and I barried it. It looks stray but I'm not sure, if it belongs to anyone.
I really love him and don't want him to be put down, but I also can't see him do this to someone else pet!

These stray dogs are getting through a physical fence? Or your dog is getting through the fence and harming other's animals? Best bet is to shore up your fence. Start concreting any holes where they or he digs at. Don't leave him out unsupervised long enough he can dig himself all the way under, and look into getting the wired electric fence that you can attach to the current physical fence and set the electric tone to beep and bite him before he gets all the way to the fence. No dog is going to continue to dig under a fence if they are getting shocked as they are doing it.

Both, he gets out and they come in. That's all I have been doing since I moved here, patching these areas, just right now I started installing underground fence at the area he digs, but it literally impossible to do that to a 2.5 acres. I'm renting this place and the landlord suggested an electric fence, but I think it might be useless because I'm pretty sure he could jump it. It's 6' tall but so many areas are no taller than 4'

There was a small nursing stray dog that keeps coming in and stealing his food. I saw her couple days ago, and gave her a treat. She took it and ran away. He wasn't happy about that. I think it was her pup because she was barking at him furiously when it was in his mouth today. I know he hunts wild rabbits but he was playing with the niegbours' small dogs at my old place.

You need one of those electric fences. Not a hotwire but an invisible fence

Build a kennel/ dog run. Reinforce the bottom edge with concrete/ pavers/ those spike things etc. He stays in the kennel if he's outside unsupervised. If he won't come when you call him, keep him leashed (even a long lead) while you're outside with him.

I'll also echo the comments about electric fence options.

Thank you all so much, I'm definitely gonna install the invisible one.

Petsafe YardMax. Make sure the collar is snug every day, they loosen over time. Use the long prongs. Do the training as suggested in the directions.