Learn Croatian: Osigurač je iskočio pa nemamo struje. - The fuse tripped, so we don't have electricity.

Yes, it is. While English uses 'tripped' or 'blew', Croatian says the fuse 'jumped out' (iskočio). If a fuse 'blew' because it burned out completely, you would use the verb pregorio instead.

Why is struje in the genitive case here instead of the accusative?

When you use nemati (not to have) to express a complete lack of an uncountable noun like struja (electricity) or voda (water), it often takes the genitive case. This acts like a partitive genitive, similar to saying 'we do not have any electricity'.

Could I use zato instead of pa to mean 'so' in this sentence?

You could, but it is much more natural to use pa. The conjunction pa is perfect for linking two events where the second is a direct, immediate consequence of the first. If you used zato, you would typically need to say i zato (and for that reason).

What is the root of the word osigurač?

It comes from the adjective siguran (safe or secure) and the verb osigurati (to secure or to insure). So an osigurač is literally a safety device.