Hi there! Congrats on your new little one!!
I'm just sort of breezing thru but wanted to answer a couple of your questions.
The marking - it's probably more a matter of he has a bladder the size of an english pea right now so he has to pee quite often. The only way you can get this under control (you need to now or it WILL turn into a problem of going back to those spots later) is to keep him confined in an area where he can't do that. Set up an xpen in the kitchen or something with room for a bed, food, water, toys, and pee pad. When he is out of the xpen, you must always be watching him so you can "catch" him and put him on the pad. Try a tether if you can't keep up with him bing loose. ALSO, be sure to get some enzyme cleaner straight away and get those quarter spots or that scent will stay there for him later...and, as I mentioned, he'll keep going back to those spots.
Anxiety when you leave is normal. He just went from being with his siblings and mom to being the only pup and then suddenly being alone while you are gone. Personally, at 13 weeks, I don't think he needs to be alone. If you could do a pet sitter or something, that would be ideal. BUT for the matter at hand, gradually desensitize him to you leaving. When you aren't really leaving, act like you are and go outside for a few minutes. Then come back in and love on him. Show him it's ok. Gradually step up how long you are outside before coming back in. And everytime you come back in love on him..even try one little treat. This will gradually teach him that you leave but you always come back. And it's a good thing because he gets loving and treats.
Gotta scoot but I know others will post to help. Hang in there. It really IS like having a human baby at first..time consuming and frustrating and a big learning curve..but you'll get it and he'll get it and it will all be worth it.
