When I pump it sometimes jams on the downward stroke so no air can pump into the inner tube – I guess a valve is sticking? How do I fix it? Is everything relevant in the head so just get a new head?

Quite possible the head's not depressing the valve core, maybe due to damage, but I have found some presta valves to jam, requiring a small push on the pin before fitting the pump head.

I've had this problem, with two Topeak track pumps. Changing the head did not solve the problem in either case. I never got to the bottom of it, although I wasn't very sure what I was looking for as the root of the problem.

I'm thinking of going for a different brand as it's a right PITA.