Is it still legal to wholesale properties in Ohio or have the laws changed requiring a real estate license in all transactions such as in the state of Illinois?

But our lender is only offering us a renovation or construction loan, which I can understand.So my questions are: should we put down as much as possible to lower the monthly payment of the reno or construction loan? 

You can always start on the lower end and increase your prices, but being realistic about your property and charging a competitive rate for the condition and location are the key to getting it rented it out, even if the goal is only to break even.

I was going through the price history and it looks like the owner tried to rent out the property between November and January, lowering the price each month until they finally decided to put it up for sale.

Reliance Property Management - They have a lower cost for their investors. 

Fannie and Freddie are playing with accepting automated valuations to save consumers costs but a computer generated appraisal might be much lower than you want as it won't account for view, upgrades, and improvements. 

It allows you to take advantage of a primary residence loan (lower interest rate and lower down payment requirements) while also becoming a landlord.

You will not get a conventional loan like owner occupied with lower down payment etc. you can get a loan but you will need 20-25% down. 

@Andrew Postell, I pulled it off the GRM site, which may not have updated ratios: "DSCR loans require borrowers to meet a minimum DSCR threshold, typically around 1.25...." https://www.rate.com/resources/what-are-non-qm-loansI spoke with a loan officer who said it may be lower now to reflect the market, so you may be right, but I am awaiting the approval and don't have the final ratio. 

Average underwriting is 50%-60%, anything lower than that is thrown out as a bad deal.