I know how to use 'would have had', but I’m really unsure about the tense. Is it past or present tense? Is it conditional?
It is "conditional perfect" as you can see from a chart at https://en.wiktionary.org/wiki/have#Conjugation. (Click on "show".)
The verb phrase would have had (would have possessed [would have had the money], would have experienced [would have had a good time]) refers to something not actual in the past (because some condition was not true).
They would have had a picnic yesterday if it hadn't rained.
But it can be used in present non-actual contexts:
I would have had enough money with me now if I had not forgotten my wallet.
I would have enough money with me now if I had not forgotten my wallet.