Is it good to keep my MacBook Pro on charge? I recently got the new MacBook Pro 2018 and would like to look after the battery better as I need it for university and would keep it for at least 3 years.

I understand that they are lithium-ion batteries and have a recommended max cycle counts of 1,000. A cycle count is counted as charging it x%, discharging x% and charging x% (if I remember).

If I were to keep the MacBook Pro on permanent charge, I will not have any extra cycle counts. However, would this cause any damage to the computer or not? I also think I read somewhere (a few years ago) about batteries breaking in (just like an engine). If this does happen, how long would this take?

If it helps, I have the 15".
These days, keeping your laptop plugged in as much as you like isn't going to make a significant difference to the battery life. The Li-ion batteries in modern MacBooks don't need calibrating, they don't suffer from the "memory" problems that NiCd batteries did, and when they hit full charge, they just allow the battery to drain by a couple of percent before trickle charging back up to 100% again.

Apple's most recent battery health tips can be found here: https://www.apple.com/batteries/maximizing-performance/