A month in the life of a rescue dog is a very short time, they're just starting to become their real selves - and a month in the life of this 5 yr old dog, who sounds like he's had a really rough life, is a drop in his big ocean. Please, first of all, go really really slowly with him. If he's lived most of his life at that kennel, then he has no clue what living in a home even entails. Where is he sleeping right now? Does he need to be crated? (Just asking - I don't crate mine). Do you crate your other dog?
I'd only start with one or two of the most important things *for now* and work on those - don't give him too much, he's having to get used to so much right now. If he plays with your dog, see if you can use your dog to help you. Don't worry so much about taking him for walks right now - that will come in time. First, get him used to having a leash on. See if you can just work on clipping it on/off - clip it on/off your other dog in front of him. And treat like crazy!! Work on that - just on/off - treat. Do that for a few days. Several times a day - clip the leash on, then unclip it. Treats - then he's free. Then - once that's conquered, time to move on. If he can handle it clipped on/off, then leave it on, and let him drag it around for a while. Then take it off. Do that several times a day for a few days, let him get used to this "thing" hanging off his neck. But make it fun, make it a party, make it come with lots of treats (I'm hoping he's food motivated). Then let him be.
Work on that - then maybe walk him around the back yard (or let him walk you - don't worry about leash manners for now) for a few min, then be finished. If possible, walk your other dog with him - walk them together (so what if it looks like a bad circus act? ) just in the yard, use lots of treats, just let him get the idea that it's all ok. With any luck, he'll see it's ok with your other dog - and they learn so much from each other. Maybe even start by leashing your other dog and letting him observe you two wandering together in the yard. Don't worry if you think he's not paying attention - he is! Start really slowly with him, he's trying to figure out so much right now, and is so overwhelmed, just take tiny baby steps with him. He's scared and is panicking when he doesn't know what else to do. You just be sure you pack all of your patience when you're dealing with him. Just keep taking loooong slooooow breaths - that in itself can help him. Look at him and make your eyes "soft" and "squinty", and blink a lot at him, yawn at him, lick your lips. He'll notice all these things (don't think he won't, trust me!).
Because he panics, I wouldn't just put him in a crate and close the door right now - for any amount of time. He's a very scared dog, and that only might make him worse. Do toss treats in, let him go in and get them, and then come out. Keep encouraging him to go in - for treats, for toys, maybe feed him in his crate. But don't rush to close him in - yet. Go really slowly with that, too.
I can't answer your question as to whether or not you're in over your head. I don't know. I do know a month isn't very long for a dog like this one to try to adapt from a life of 5 years in a kennel to a life in a real home. My guess is he's overwhelmed and hasn't acquired the skills (yet) to adjust to life "outside". I would also bet that with loads of patience and love, he will. He's just going to need to move only as fast as he can . Use your other dog, show him what life can be like - but go almost painfully slowly. One tiny baby step at a time. Some days may be one step forward and two steps back - and others may be one giant leap forward. But my bet's on the dog, he'll be ok.