Heating Help

Why is heating and pump on when CH is turned off?

I rent and have a gas fueled Rayburn that provides hot water and central heating. I have a couple of problems with it and the landlord is useless, if anyone has any suggestions I would much appreciate it.

These are the issues:

1) The pump runs fairly frequently, even when I have not used any water. This is the most annoying problem because it is noisy (often wakes me up at night) and seems to be at the root of a higher than necessary electricity bill. It's an older pump with three speeds, I have it set on speed I at the moment but have tried the other settings and it made no difference. Can I just turn the pump off, at least overnight?

2) There is always (scaldingly) hot water, even when the HW is on a timer and switched off. This is more just odd than a problem but I wonder if it's connected to the pump running so much?

3) The CH/HW will turn on at the correct time if I set the timer but it doesn't turn off automatically at the end time.

4) The upstairs radiators get hot even when the CH is off.

In case it's relevant I live in small (one room + bathroom upstairs, one room downstairs) building which has three radiators in total.