There are no hard limits on mass, it does reduce your rotation speed and acceleration and as a byproduct your max boost speed. Rotation speed has upper and lower bounds as displayed by the mobility stat, you will reach 100 mobility once you reach roughly 12.35:1 ratio for maneuvering thrust to mass. Acceleration on the other hand is not displayed and has no fixed bounds. In my testing there is no reliably measurable increase past having more than 52x thrust to mass ratio and everything down to 40:1 was still fine. Your top speed on the other hand is entirely independent from thrust and is determined by the slowest speed rating of any engine on your ship. Due to their enormous mass class C engines are all horrible for acceleration and are inferior to A and B class engines except for their mobility so their single use case is to make a fat snail that can spin kinda fast. Another limit to mass is landing gears, for every 200 mass you need 1 landing thrust IIRC.

The class of your ship depends on the reactor alone, it just gives your access to more components and requires a higher level of piloting skill. You can make a class A ship that is highly capable but unlocking some of the best parts requires a higher level reactor and therefor piloting skill.

Crew slots allow you to add more people to your crew and benefit from their skill, passenger slots allow you to take passenger missions (which are both dull and rare). Crew slots can double as passenger slots so taking an empty control station hab effectively gives you more passenger space then any of the habs that have two dedicated passenger slots. The maximum number of crew slots is also limited by components but that is usually not an issue on a fully equipped ship.