I'm replacing my old pump with a variable speed pump to save on electricity costs. I'm new to pool plumbing, but from what I gathered watching a few videos, everything is glued together and people usually just cut pipes and add couplings when replacing equipment. The problem with my setup is that I'm pretty sure it's been done already in the past, so I don't really have much room to cut anything. Here's a picture of my existing setup, with the new pump placed on the side. The inlet is on the same height as the existing pump, so I will be able to keep it on the slap, but the outlet is further back, so I will need to move the vertical pipe a few inches towards the back:

My questions is, where should I cut (or perhaps unglue?) old pipes in order to make new connections? I'm posting my current plan below. The pipes are 2.5" ID. I want to cut at the marked locations and then glue an elbow at the top cut and a coupling at the bottom cut. Is that the right approach here, or should I attempt ungluing an old connection first closer to the pump, and only if that fails, go with the cut approach?

I also have a question about this little spigot. What's the purpose of it, should I incorporate one in rebuilt version?

Any help/advice would be appreciated!

My questions is, where should I cut (or perhaps unglue?) old pipes in order to make new connections? I'm posting my current plan below. The pipes are 2.5" ID. I want to cut at the marked locations and then glue an elbow at the top cut and a coupling at the bottom cut. Is that the right approach here, or should I attempt ungluing an old connection first closer to the pump, and only if that fails, go with the cut approach?

I also have a question about this little spigot. What's the purpose of it, should I incorporate one in rebuilt version?

Any help/advice would be appreciated!