It sounds like this is a combi boiler you have, and perhaps you live in a hard water area.
The sticking taps are I think either very worn, or possibly scaled up with lime (or both). Perhaps they are older than the boiler and are not coping well with the extra pressure a combi gives.
They are probably the type with a capstan head that screws up and down by several turns between off and on. It is tiresome to take taps right off and replace them, as it involves lying on your back and squeezing under baths, while trying to undo nuts you can't see, so consider learning to take them apart, clean, rewasher and reassemble with silicone grease on the moving parts and PTFE tape on the gland and screw threads. This can all be done from above, and once you learn how, you will enjoy it so much that you'll want to do all the taps in the house. Or you can fit tap revivers at higher cost, which swap the working parts of the tap and the capstan head, for new ones.
But if you employ a plumber, fit new taps throughout. Bristan taps are especially good. Unnamed imports, especially if they are ceramic taps with a quarter-turn from off to on, may need replacement parts that are unobtainable.
The other problem you describe, about the temperature of the water from the hot taps varying when other hot or cold taps are turned on an off, is due to the flow switch in the boiler reacting to the hot water flow, which varies when taps are turned on. Perhaps it is also worn or scaly. A boiler engineer can replace it. He may also comment on other aspects of the boiler, ask if the heat exchanger seems scaled or dirty, and ask him to test the dynamic flow of your incoming water supply. It should be in the region of 12 to 20 litres per minute. More flow is better than less.
If the pressure is excessively high, your taps may wear out faster.
Vaillant is a good brand of boiler. Ask whoever normally services it to take a look. Boiler engineers have a much higher hourly rate than plumbers, so if you can find a well-recommended and experienced plumber, ask her to do the taps.
Opinions differ, but I am not a combi enthusiast, and would argue that these problems would not occur with a cylinder-based system.