Should have things like purchase price, financing, contingencies etc.

In fact, I have heard some investors who make offers contingent on interest rates, if they go higher, the offer gets lower.

You'll also have extra costs for your 203k, such as an additional orig fee from the lender, contingency reserve for rehab (10%-20% of rehab costs), inspection fees, title update fees, etc. 

I'm working a contingency on if I have to replace the roof because I believe the seller won't have the cash to replace the roof.

Should I find a new property and put in an offer before selling my rental, and make the offer contingent on selling my rental?

I can sell grandma's house today for $400K, the traditional way with appraisals, inspections, showings, repairs, staging, financing contingencies, all all the rest, OR.....we have an investor who can pay you CASH today without all that, but it will be at a discount...$300K to transfer all the risks and inconveniences to that investor.   

The property was listed at $675k, so we ended up being $65k over ask ($740K) after some back and forth, waived our appraisal contingency, covered Title Insurance, and did a 2 week close.

One will be all cash offer and the second would be with a conventional loan contingency.

If you have the normal contingencies, have an inspection done.

Our Bridge loans are currently lower than HELOC rates2) Get a HELOC now and have it ready3) Save up at least 5% of your own cash and you can buy non contingent, if your debt to income ratio is low enough4) Make offers to buy a new home, contingent on the sale of your current home.