Is there a way I can influence what types of scientists I will get in the first few years?
No, only how many you get (by building more naval academies).It really
Assuming that I don't have good CP scientist, should I assign a scientist with a large bonus to another field to it or rather a scientist with a 0% bonus?
For such a vital tech probably, but scientists do get better over time (both from actually researching and simply existing, but the former is much faster) so for more minor techs I tend to use worse scientists with the appropriate field, because it doesn't take much for them to be better than the off-spec scientist.
3. Where to establish a colony?
Mars is fine for just getting a colony going, even if there are no resources having population spread out increases the rate at which it grows. Additionally, yes civilian shipping will start going backwards and forwards, first transporting colonists and infrastructure and then (as the colony grows) standard trade goods. Since Mars is very close to Earth those trades tend to complete quickly, giving your shipping lines a lot of money, which means they get more ships and become more useful faster (which can potentially be a bad thing, later on when you have so many civilian ships it's notably impacting performance).
I guess I should have rather build a commercial SY, right?
For building a freighter? Yes. Commercial SYs are much cheaper and faster to expand. On the bright side, now you have a 30kt naval yard you can use to build warships.
And how do I use this ship to transport a larger amount of cargo?
Either cycling orders (if you just want it to do its task indefinitely, such as if you have a tanker transporting fuel from fuel harvesters to a colony) or repeating orders (if you want it to do it a set number of times and then stop). Sounds like the latter in this case, but be wary of off by one errors when you're repeating the orders, the number you input is how many
extra times it will repeat the order, so if you want it to do something 100 times put in one cycle and then repeat 99 times.
How should the ship that enters the first new system be desgined?
Depends a lot on what you want to do, and what the objective of your game is. Just want to find what's in a system, not really caring about what it is specifically? Throwaway survey ships. Trying to defeat every NPR you come across as quickly as possible? Large battlefleet. There's not really an answer that's always applicable to every situation.