Question about subject verb agreement...?

The second sentence is correct.

This is a case where the word 'man' has been left out, or "ellipted". When you include the missing (ellipted) word, the sentence reads 'The first man and the second man...'. No matter which way you look at it, there are still two men, therefore the verb must agree with the plural state of the subject.

To put it another way: 'The first and the second man' are two 'men', regardless of who is first and who is second. 'The men' requires the verb to agree in the plural, so: 'The men were happy', and therefore 'The first and the second man were so happy.' is correct, and '...was happy' is not correct.

Please note: the first sentence is very awkward and does not sound like a sentence a native speaker of English would produce. A native English speaker is more likely to say 'The two men were so happy' or 'Those two men were so happy'.

Neither sentence is great, but the 2nd one is better. Try this one: Both of the first two men were very happy.

The second one... the conjunction 'and' makes the subject of the sentence plural... not one or the other but BOTH men.

The second one is correct, because although they're both the subject, they're separate entities. So they were happy, because there is two of them.

the second one is correct.