First time RE investor. Please poke holes in my strategy!

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I've (29M) about $250k saved up. Don't own a home yet, but I've been planning to buy one for a while now. Instead of buying a single family home, I'm thinking of buying a condo outright in cash, rent it out so I can start generating cash flow/passive income and then do cash out refinance or HELOC to pull equity out of the condo and use that as a downpayment for a single family home about half an hour away. From what I've read online, I can pull up to 80% from the value of the condo so about $200k. I'll use that to buy a SFH in the ~$400k - $500k range. I understand that I can probably better use my cash but I'm very risk averse. Basic math is as follows:

Cost of condo = $250k, Rent estimate = $2k, HOA + taxes = ~$800. Net profit = ~$1200.

Cost of SFH = $500k, Mortgage + taxes = ~$2500 (assuming I use $200k from cash out refinance as downpayment)

Hence, net payment on the mortgage out of my pocket would be ~$1300, which I’m very comfortable with.

Location = NJ, Income = $100k, Debt = $5K in student loans. Credit score = 720+

PS - The Condo is recently renovated. 

My questions are:

1. How soon can I pull equity out the condo once I buy it? Is there a "waiting period" before I can do a cash out refinance? I understand I've to wait 6 months to do a traditional cash out refinance. But can I go the Delayed Financing route to immediately pull out my money? I read Fannie Mae's guide about this, but I'm confused about on of the criteria in order to quality. The website says "The new loan amount can be no more than the actual documented amount of the borrower's initial investment in purchasing the property plus the financing of closing costs, prepaid fees, and points on the new mortgage loan (subject to the maximum LTV, CLTV, and HCLTV ratios for the cash-out transaction based on the current appraised value)." I'm not sure what this implies? Does this mean that the new loan on my primary residence/SFH cannot be more than the price of the condo, so essentially cant be more than $250k? Am I understanding this right?
2. On what grounds can a bank/lender not approve a cash out refinance, if any?
3. What are potential risks with this strategy that I may not be aware of? I understand being a landlord is not easy, but I’m okay with all the headache that comes with managing tenants/property. 
4. Any other suggestions to stretch my cash in order to generate passive/rental income? 

Please poke holes so I’m aware of any unwanted risks that I’m potentially taking with this entire strategy. My entire point is to somehow generate rental income that can offset my mortgage payments on my primary residence.Thank you!