Basically, yes to all of your questions with one mod. You can use a no-hub connector. This is a rubber sleeve with metal banding around it to keep the pipes in alignment. The ones that are a thick rubber sleeve with just clamps at the end are only supposed to be used when burried and both ends can be supported. Otherwise, the thing won't hold both ends in alignment, and it can act as a catch point for clogs. You might be in the market to replace all of the drain lines. Depending on where you live, running the drain line outside can be a problem, as it can freeze up and create problems.