You removed some questions such as “What happens if some nodes go temporarily offline?” or “What discourages from running big nodes and overtaking the network?”. Would you mind explaining us what made you do so?
The first question was rephrased to "What would happen if some nodes went temporarily offline?". As for the other one, I believe I wanted to include the answer to it in some other question. I will fix that later.
Also, what prevents someone from allowing free transactions (not even for 1 sat per tx)?
Nothing. Currently, I have two channels which have zero fees and it's been a while since I routed any transaction. You are more likely to end up with an unbalanced channel if you don't set any fees.