Learn Turkish: Mahkemede yemin zorunludur. - An oath is compulsory in court.

The -dir or -dur suffix acts as the 'to be' verb for general facts, official statements, and objective truths. Because this is a legal fact, using zorunludur sounds much more formal and definitive than just saying zorunlu.

Could I say mecburidir instead of zorunludur?

Yes, mecburi is an Arabic-derived synonym for zorunlu (which is of Turkic origin). Both mean compulsory or mandatory and are completely interchangeable in this legal context.

Why doesn't the sentence say bir yemin for 'an oath'?

In Turkish, when making a general, categorical statement about a concept rather than a specific single instance, the word bir is omitted. Adding bir would make it sound like one specific oath is required, rather than the general act of swearing an oath.

If I want to say 'to swear an oath', what verb do I use with yemin?

You use the auxiliary verb etmek. To swear an oath or to vow in court is yemin etmek.