I'm considering to buy a 20 watt charger for my iOS-devices. Obviously it charges a device two to three times faster then the 5 watt chargers, which I currently use.
I'm not sure about that, the BMS on the iOS device should alter its power draw to match what it's programmed to accept, given the current state of the battery.
If 5 W is the most it can charge at, then plugging it into a 20 W charger isn't going to force more than 5 W in.
If your device is capable of drawing more than your current charger provides then you'll see some improvements in charge time with a higher capacity charger but not necessarily by the ratio of how many watts the new charger provides vs the old one, ie. 20/5 = 4x faster. The BMS has to accept 20 W and even then things are a bit more nuanced as 20 W would be the maximum, not continual power draw.
Might it reduce the life-time of the battery? Or is it even dangerous (strong heating up, explosions)?
It really shouldn't, unless there's an existing flaw in the battery or charger.
Should I definitely get an original Apple charger? Or are others vendors safe too?
I think that's going to be tough to get a definite answer for unless you have a teardown on the specific device, from someone qualified to comment on its quality. I've seen some teardowns of USB chargers with terrible isolation and there have been cases of people being shocked while using their phone as it's charging.
I'd put money on there being plenty of properly made, safe chargers out there. The question I ask myself is: do I feel safe plugging a $1,000+ phone into this to save a few dollars, or is my peace of mind worth the ~$30 for an OEM part that I've seen a teardown confirm that at least the design is sound?