He says we're good to go except there is an open plumbing permit that needs closed out - says the plumbing inspector probably just forgot to do the paperwork.

That 600/month will quickly evaporate with your first pest control and plumbing call.  

Need to redo the plumbing and take out the copper pipes in my 3 family house I recently bought..... how much should I expect it to cost?

However, if your renter has rented from an apartment community in the past that is professionally managed, it is likely that they've had the clogged toilets as a service their maintenance team would handle.Along Chris's point, you don't want your resident fixing plumbing issues like broken sinks and toilets because they could make the problem worse. 

Just recommending you verify electrical and plumbing systems are up to code.  

as an electrician I am wondering what year this is and how you estimated the electrical/hvac/plumbing costs.

Fixing this may cause plumbing issues like the engineer said due to drainage issues or cracking the pipes when the house move back to level breaking the seal at the joints.  

This would be a fee for building, elec, plumbing ext. $67.00 per permit.

Do you know how to fix plumbing issues, install new locks, install ceiling fans, stuff like that?    

I guesstimate approximately $35K to $45K to completely redo the roof, replace and repair the dry rotted base house frame sitting on the foundation (sills, floor joists and subfloor), outside brick repair, new drive ways and electrical and plumbing updates.The average selling price for well-maintained and updated duplexes similar in design in the area are $85K to $105K.