As I understand it, if a mining operator was to attain 51% of the network, they can perform a double spend. But would this be detected? And if the same attack was done on Zcash, could it be detected also?

This is one thing they could do, yes.

But would this be detected?

You cannot detect a 51% attack occurring. To perform a 51% attack, you'd have to mine a secret chain with greater difficulty than the main chain, then replay this secret chain on the main network. Only at the point of replaying can this attack be observed, as this would cause a massive reorg on the main chain. To sustain the attack, the attacker would then have to continuously mine at greater than 51% of the total network. The damage will have already been done though.

And if the same attack was done on Zcash, could it be detected also?

Same answer as above.

What other potential abuse can a 51% mining entity cause?

Censoring transactions, double-spends, delayed tx processing, spam the network... just a few things that immediately spring to mind.

As I understand it, if a mining operator was to attain 51% of the network, they can perform a double spend.

This is one thing they could do, yes.

But would this be detected?

You cannot detect a 51% attack occurring. To perform a 51% attack, you'd have to mine a secret chain with greater difficulty than the main chain, then replay this secret chain on the main network. Only at the point of replaying can this attack be observed, as this would cause a massive reorg on the main chain. To sustain the attack, the attacker would then have to continuously mine at greater than 51% of the total network. The damage will have already been done though.

And if the same attack was done on Zcash, could it be detected also?

Same answer as above.

What other potential abuse can a 51% mining entity cause?

Censoring transactions, double-spends, delayed tx processing, spam the network... just a few things that immediately spring to mind.