I haven't a clue how to bleed a radiator. We didn't have them growing up so I never had reason to learn.
Also, I think if you wanted him to fix your dishwasher/kitchen problem (because it is your problem. You own the property. When they move, they aren't taking this lovely new fitted kitchen with them) then you would have to expect to either pay him in his professional capacity or reduce their rent that month. And of course, you might have someone you know who might do it better, or cheaper than he would charge.
My DH is an engineer and can fix many things around the house, but as we're paying rent to someone else, we would expect compensation if he did. And if something went wrong in the process of fixing something, he would probably be liable for whatever the damage was, and we don't see the need to have that potential problem.
Our front door also had this sticking problem. It wasn't just "stuck" as in, oh it takes a bit of a nudge to open, I literally couldn't open it without fully putting the force of my entire body on it. This is not fun when you're trying to get in with bags of groceries or a baby in your arms, etc. It's not just a minor inconvenience. 
Anyway, I wouldn't get them carpet unless you want the house carpeted. If you do want the house carpeted, then maybe offer to share the cost.
You're a first time LL so it's a learning process for you. If you resent the amount of rent you are charging him, then you should increase it, or consider an increase for the next tenant.
And definitely test major purchases before their warranty runs out. I'm surprised 5 months was too long to get the fitters to fix it, surely it would have been obvious it was their mistake?