Do I have to wait for the purchase contract to apply for a mortgage loan?
Technically speaking you do need a contract to apply for a mortgage. However you can get pre-qualified for a loan prior to signing a purchase contract.

What will it take to subordinate a second mortgage? Does it require a certain LTV?
The subordination will be approved or denied by the mortgage company who is holding the second mortgage. The higher the LTV the harder it gets to get a subordination. If you are at 95% CLTV (combined LTV) the second mortgage company will carry a higher risk of foreclosure.