One of my boys had problems with his pads being cut up / irritated as well. When I brought him to the vet they recommended to use Bag Balm on them which I did and it helped a lot! It's best to put it on them right before bed time so it'll really soak in while they're sleeping. You can try putting on some light socks (maybe baby socks) if he'll tolerate it just to ensure they don't lick it all off. Mine wouldn't tolerate having socks his feet.
As far as seperation anxiety, you can try to help him to get over this by showing him that you'll always come back. Start out with putting him the crate and then go into the other room for a couple of minutes. When you go back in to him, reward him and give him a treat. With time you can gradually increase the amount of time you leave him alone, but always be sure to reward and treat him when you come back in. This is how I trained both of my boys and they both responded very well to it.
One last thing I wanted to mention. I understand that you live in an apartment so getting exercise may be a bit more difficult for you, but at 5 months old your puppy shouldn't be doing much running (at least not on a leash). He's still very young so his skeleton and joints are still developing. This type of forced exercise may cause more harm than good. Doing a search on 'forced exercise' will bring up several threads where this has been discussed before.