No heat or hot Water?

Not likely the pump as the boiler is firing. Sounds like flame ionisation or pcb fault. Would need to be onsite to give a proper diagnosis.

There could be air in system or faulty pump or motorised valve on conventional system. Otherwise a fault related to boiler.

there are so many things it could be get a gas safe plumber to look at it for you.

could be the pump not moving the heat away from the boiler, could be a few different things. you need to get a gas safe registered engineer to have a look

Your boiler has to prove that many devices work before ignition takes place, for example: 1. Pump 2. Fan (if fitted) 3. Air pressure switch (if fitted) 4. Gas valve operating 5. If all of the previous are functioning correctly then the last stage is ignition, so if boiler burner fails to ignite then as all answers have previously stated you need a Gas Safe engineer who specialises in breakdowns to attend to carry out diagnostics!

This answer cannot be much help but as said before by other tradesman, best to call an engineer out to check it for you. Could be a simple thing or multiple faults depending on the age of the boiler and service intervals.