It is your model and you may paint it any way you wish. The plastic police will not break down your door at 2am for painting your model as you have described.
There are no known color photos of the PT-109. There are color photos of other PT boats later in the war in a green pattern camouflage. The boats were delivered to the Navy at the ELCO plant in Bayonne painted in an overall gray with a dark gray deck - not bare wood.
It has been determined, and generally accepted that the boats in Kennedy's squadron in the South Pacific were painted overall in theater in a home-brewed green paint. White Ensign's Colourcoat line of paints includes this color. It is not an olive. If you must choose a paint which you have in your paint box -- go with a forest green.
The hull bottom was painted in Copperoyd - a trademarked antifouling paint. It was a rusty-red color. Lowe's Hardware store sells American Tradition paint - their Red Primer is a good match. Out of the bottle - a 60:40 mix of Testors Rust and Insignia Red will get you close.
I'll give you the raft in gray.
On to the torpedo tubes ... the domed tip on the tube is a protective cap that blows off when the torpedo is launched. It is not the tip of the torpedo. It should be the color of the rest of the boat. However, since these are expendable items they could come from the warehouse in almost any color - grey or another green.
The back end of the torped tube wasn't open. It was a door through which the back of the torpedo was serviced. It was hinged to swing inboard and held in place by a spiderweb of braces and thumbscrews. It should be the hull color
You may not want to hsue the big numbers on the hull. They were applied to the PT boat in President Kennedy's inagural parade. The myth that they were there sorta stuck. Use only the numbers on the front & sides of the chart room. I'm not sure about a number on the pedestal of the aft 20mm gun at the time of her loss, but they were there when she was put on a tanker to be shipped to the South Pacific as deck cargo.
You may want to search through this MB for other threads on PT boats in general and PT109 in specific