In mi you cant tie the ejector vent or (stink) pipe in to the exsitinng house vent and it has to be a 3 inch pipe one foot above the hole in the roof and one foot below the roof before you off set but in a non frost state you can use a smaller pipe than a 3 inch pipe for the vent out the roof and I would go with pvc schedule 40 for all of it but some people use sch 30 for the vent because its cheeper also depends on the length of the run for proper sizing of the pipe hope this helps
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