Hi there and welcome! With carpet and the details you have on it, it sounds like it’s been installed for about 8-10 years. A good carpets life is estimated at around that time frame. You could try and get it professionally cleaned to stretch the life a bit more, but it just depends on how bad it is. That laminate that has bubbled and peeled will do just that when in contact with water. I would recommend replacing it with a vinyl plank flooring. Much better stuff and waterproof.
In reguards to charging the previous tenants. You MAY be able to get them for neglecting to remove water and or shoes while walking on the laminate. All this kinda depends on when it was put in though as it may be past it’s expected lifetime.
Id charge them a fair price for any cleaning and yard work as long as it stated in the lease that it was the tenants responsibility.
Welcome to the landlord life. This will happen. Just do your best to make the process easy for you. I highly recommend getting a tried and true lease. I do believe Real Property Management Last Frontier has one for purchase.
Best of luck!