Does anyone say the phrases "Pasensiya," "Paumanhin," or "Patawa

You need to be fluent in Tagalog to use phrases "pasensiya", "Paumanhin" or "patawad" as this is very critical to express sincerity. Otherwise, you can just say "sorry' or "excuse me"
"Patawad "should only be used if you are asking for forgiveness.
"Pasensya" is a casual way to say sorry.
"Paumanhin "is for 'excuse me".

Pasensya = sorry
Paumanhin = Also sorry (I never hear this word)
Patawad = Kinda like you're talking to God. I only ever hear it in Religious contexts.

@matthewreichle "pasensya na" is still commonly use "patawad" is a very serious word it denotes complete humility and acceptance of guilt. It is not as common as the English term "sorry". ^_^

Patawad in its deep meaning is to ask for forgiveness, from someone you have seriously aggrieved. To say "patawarin niyo po ako" is saying please forgive me (for some serious violation). It's appropriate for asking God's forgiveness, or asking for mercy.Sometimes, during haggling, it is used as in "give me more of a discount (or a better deal)".