I have to come to the table with 34,000 and the lender will provide the funds to rehab which I will not use so I can pull the equity out of the home during refinance.I have used the calculator and not sure if the numbers was accurate. 

Consider finding a partner who can bring the entire purchase price to the table so you can use your funds for the rehab, especially with your background in construction - you should be able to accurately predict and control for construction costs.

@Joyce Jackson I have no doubt that some Section 8 landlords charge a form of “under the table” rent.

If I can bring a check to the closing table, what scenario exactly is the bank, if they still believe the asset (house) will appreciate and still be good collateral, trying to avoid that having zero equity would cause  if the problem of closing costs being covered is solved?

You can do all that, but if surface water runs into the house (bad design) then you're fighting a losing battle.If it is, I'd ask about exterior drainage, like a French drain around the perimeter or fixing the grade.  

Wow, that table looks a lot better in preview than it does when rendered!

The new furniture will be mid century modern furniture, including a sectional sofa, TV stand, armed chair and a coffee table. 

I would be happy to host a virtual meet up for Greater Montreal Area folks - English and French welcome.My brother and I have each done Single Family homes for the last few years but just acquired our first multiplex together this week.  

The lender needs to know way before the closing table that you have enough to purchase the amount in your bank account (including Closing Costs), another issue that they'll would have even if you could do that is projecting DTI due to that high balance as soon as you close on your credit.

Just get all expectations including yours on the table so everybody stays happy.