I would advise a cash-out refi instead however, it may or may not make sense for you to be comfortable with a HELOC all you have to do is read the terms and understand what they mean to you and your plans however, if you do use a HELOC I would ensure I knew the rate floor (the lowest it can go) and the rate ceiling (the highest it can go) and how often they can raise the rate by how much  each time.

Drop ceiling in basement needs redone.Whole interior needs painting/patching. 

Now all that's left is replacing ceiling tiles in the basement.

If you discover multiple layers of plaster and/or no insulation I would budget a reserve to gut each apartment back to the studs as they turn over and insulate {We've found spray foam to work best in the older houses, especially if they have rough-cut framing and sheeting}.I am partway though this process with one of my buildings that is 120yrs old ... only I am stripping all walls back to the studs and dropping the ceilings as well.

Hello, we are doing a couple high end homes and would like to know your thoughts on ceiling textures.

one thing I would want to be sure of is the texture on the ceiling. 

New Ceiling and paint at my expense.

This would save money in numerous places of the construction and also enable the builder to have vaulted ceilings and such since there would be no mechanicals or ducts in the attic. 

Not a lot, but just a bit,  This could be a big deal or not a big deal.There is a bit of black mold on the ceiling near the brick chimney that vents the furnace.

Is it worth it to "finish" the basement with drywall walls and a ceiling to make the space feel more like a family space and less like a basement?