Also, do you guys use apps such as cashapp or venmo to collect rent?

Would not having work history like taxes or proof of income stop me from purchasing a house with any type of mortgages?   

The owner is willing to carry the property while I do the repairs, when we sell he would then collect his $250k( the original value we determined I would pay) plus a small percentage of profit (yet to be determined). 

@Trevor Dominique -- my initial thoughtsWhat are the current (as-is) operating financials; physical occupancy, economic occupancy, revenue, expense, collections, aging, etc?

You inputted a rehab of  2 months, so you collect 10 months of income for the first year. 

Been collecting rent and claiming interest and expenses on tax returns per terms on the contract.

Because I am a teacher and don't get paid over the summer, I would need to identify the replacement property while the relinquish property is in the process of closing, rather than waiting until after it closes, so that I can continue to provide proof of income to the loan officer to secure a mortgage on the replacement property.

So day one, you are only collecting $1000/month in rent.

You'll be the legal owner and will be collecting rental income, so I think you will be able to utilize the common strategies of depreciating the property and CapEx, expensing repairs and other property-related out of pocket costs, as well as interest on the mortgage loan. 

You can do either.If you're just getting into the real estate game, then it's probably a good idea to speak with some lenders first as @Jaron Walling suggested.How far along you get in the process will be somewhat limited if you don't have a deal, but the conversations are still likely to be valuable.Additionally, some HMLs can offer a proof of funds, which can be helpful while making offers.Best,Michael