Did Parris wanted the deed to his house, firewood, and more money?

Yes.... all true.

Parris: Where is my wood? My contract provides I be supplied with all my firewood. I am waiting since November for a stick, and even in November I had to show my frostbitten hands like some London beggar!

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Proctor: Mr. Parris, you are the first minister ever did demand the deed to this house -
Parris: Man! Don’’t a minister deserve a house to live in?
Proctor: To live in, yes. But to ask ownership is like you shall own the meeting house itself; the last meeting I were at you spoke so long on deeds and mortgages I thought it were an auction.

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Parris: I regard that six pound as part of my salary. I am paid little enough without I spend six pound on firewood.
Proctor: Sixty, plus six for firewood -
PARRis: The salary is sixty-six pound, Mr. Proctor! I am not some preaching farmer with a book under my arm; I am a graduate of Harvard College.