Here're two blog posts that are better as a starting point:https://www.biggerpockets.com/...https://www.biggerpockets.com/...BP published two books on real estate taxation, and there're dozens more on Amazon.

Thinking Outloud here...Use a LLC with flow-thru taxation (not S-Corp taxation).Give your company a loan which is the HELOC.Pay HELOC back (loan is an expense for the company).Interest on HELOC is deductible.

May not happen, but you should be prepared for the taxes to go up.The taxing authorities are supposed to tax at market value....but don't tell you how they get there.They do have access to MLS, but they also have plenty of other estimation tools.I think by law they have to look at least every 3 years at values and modify assessments to match market value, but in reality the bigger counties will probably do it every year.

Please recommend an accounting firm for book keeping and filing taxes for LLC and contractors for a group home (operating from Laveen/Phoenix)

Find one who specializes in real estate taxation. 

Here’s the question:If, say a year after the cash-out refi, the home is sold for $350,000, would you pay tax on the current difference of $150,000 ($350,000 sale price-$200,000 current amount owed)Or,Would the IRS think you’re trying to evade taxation and tax you on the sale price-the amount owed at the time of the cash-out refi ($350,000-$75,000)?

.- being in the personal name is not going to be relevant for the rental properties from a taxation perspective for you. 

Like why subject yourself to two layers of taxation with the intent of distributing profits too here....

You will pay tax at ordinary income rates to NY State, that's for sure.   

Most taxing bodies tax at least 1% of value. 680k*.01=$6800 per year.