I have a 700sq.ft. home with one bath, Will the roof vent at the washer be enough to vent the sewer?

I have a 700sq.ft. home with one bath, Will the roof vent at the washer be enough to vent the sewer? Every fixture that has a trap MUST have a vent. Your washer vent won't vent the entire house. It's plain to me that you're concerned about something but I'm not sure exactly what. Can you list your concerns in detail for me. Back to you, Tom

Every fixture that has a trap MUST have a vent. Your washer vent won't vent the entire house. It's plain to me that you're concerned about something but I'm not sure exactly what. Can you list your concerns in detail for me. Back to you, Tom

gas smell and not enough vents is my major concern. Can I add vents by going straight out and then up above roofline?
The overhang is only 14" is that enough room?

Can I add vents by going straight out and then up above roofline? Will you be pulling a permit for this job? #Explain to me exactly just how you're going to run the vent starting at the trap of each fixture, I'll start you off. First you must open up the wall and remove the elbo connecting the stub out and replace it with a sanitary tee. You take it from there. Good luck, Tom

Will you be pulling a permit for this job? #Explain to me exactly just how you're going to run the vent starting at the trap of each fixture, I'll start you off. First you must open up the wall and remove the elbo connecting the stub out and replace it with a sanitary tee. You take it from there. Good luck, Tom

From the tee i will go up with pipe to be above the trap then elbow out of the house and elbow up then pipe up thru the roof adding a (roof flange?) to run the pipe approx. 6" above roofline.
correct?
Can I paint this line to match the back of house?

From the tee i will go up with pipe to be above the trap then elbow out of the house and elbow up then pipe up thru the roof adding a (roof flange?) to run the pipe approx. 6" above roofline. Sounds good to me, Don't forget to slope the vent back from the roof 1/4" to the foot. Be careful not to allow any "bells" in the vent that could trap water. Maintain a constant slope.
Yes, you may paint the pipe. Good luck, Tom