Assumed I am in a train or car (only co-driver!) with high speeds. Can I catch Pokémon anyway although my environment passes very quickly?
Yes this is possible, after tapping the Pokémon, your movement speed does not affect the catching period.
I have been catching them during hi-speed train travels myself without any problems so far.
Since the last update, Pokémon spawn rates during high speed travel have been reduced significantly. This to prevent people from playing and driving. The limit seems to be somewhere between 60 and 70 Km/h. During travels between 15 Km/h and 60 Km/h a reduced catch rate is observed as well, in combination with a higher escape rate.
TL;DR: It is still possible to catch Pokémon while moving fast, up till certain speeds, and with reduced efficiency.
In Ingress there is a speed limit for particular actions. To be able to hack or attack a portal, or place a resonator onto a portal you'll have to move at maximum around 25-30 km/h and to collect energy you'll have to move at maximum around 70-80 km/h. I'm pretty sure that Niantic will limit speed in Pokemon GO, too.
Also in Ingress turning off and on GPS is considered as cheating. My guess is that this would be checked in Pokemon Go, too.
If they haven't set controls for these limitations yet, they most probably will do it in near future.
Past a certain speed, your radar won't be able to detect nearby Pokemons as effectively (or at all). For me, detecting Pokemons worked well in slow public transport such as city buses, but stopped for regional trains for example, except when the train was slowing down and approaching a station.
However, once a Pokemon is detected and the fight is started, you can catch it independently from the speed.
Also note that Egg Hatching will generally not work inside a public transport, since it uses a combination of GPS and pedometer to calculate the distance you've walked (so it will notice that you are not actually walking).
Last weekend, 9/3/16, I went on a two hour road trip. My husband was driving. When we were going about 70 mph I was able to engage pokemon, but after catching in a pokeball, 9 out of 9 escaped and ran away. I use to be able to catch them when we went on this trip, but since every one ran away, I don't think you can anymore.