I've been looking at cash-out refi options to put that equity towards purchasing more investment property(ies). 

But because a certain unsophisticated part of the populace believes he possesses hundreds of millions of dollars, he is targeting for lawsuits by the attorneys general of at least 3 states, as well as two private law firms trying to put together class action suits.

The space is way smaller than I thought once I put my stuff in and I can’t even fit everything I need.

If that is too low for them then you've put the ball in their court for them to give you a number they are thinking. 

I'd prefer to put a downpayment than do all cash. 

You forgot to put your location in your profile and your post so the answer is unknowable.

If it takes too long to complete, mistakes are made, the wrong people are hired, money is put into repairs that do not pay off and so on you can lose money. 

Some say that I can sell it "as is"3- Not having permit for these work, would it affect whether I can put it on short term rental?

Put together a proforma and determine whether the deal will cash flow to your standards.

I would put no other assets into this entity such that, if it is sued, there is nothing to lose.