Haya?
"Estoy contento de que no haya llovido durante tu partido."
"Es una pena que te hayan robado el bolso."

I'm pretty sure these could be translated as:
"I'm happy that there wasn't rain during your match."
"It's a shame that they stole your purse."

I just don't understand why "haya[n]" is used. If present tense of raining is "está lloviendo" wouldn't the past tense be "estaba/estuvo lloviendo"? How is "haya" changing the sentence?
For the second sentence, how is this different from if they said "... pena que te robaron..." ?

Also, this is "Latin American Spanish," if that matters at all.
Gracias por la ayuda.

Question

Haya?
"Estoy contento de que no haya llovido durante tu partido."
"Es una pena que te hayan robado el bolso."

I'm pretty sure these could be translated as:
"I'm happy that there wasn't rain during your match."
"It's a shame that they stole your purse."

I just don't understand why "haya[n]" is used.  If present tense of raining is "está lloviendo" wouldn't the past tense be "estaba/estuvo lloviendo"?  How is "haya" changing the sentence?
For the second sentence, how is this different from if they said "... pena que te robaron..." ?

Also, this is "Latin American Spanish," if that matters at all.
Gracias por la ayuda.

Answer

You’ve translated correctly, and it’s standard Spanish, not a Latin American thing.

“Haya” is the present subjunctive of “haber” used to form the present perfect subjunctive. It serves the same purpose as the present subjunctive, but is used to talk about actions completed in the past (i.e. “perfect”). In your examples, we use the subjunctive since the speaker is talking about his emotional reactions to the facts, rather than the facts themselves. It’s also possible to use the imperfect subjunctive (lloviera / lloviese) to talk about the past, but this would conceive of the actions as unfinished.