a few newbie questions about renting out the property

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Dear all,

I just bought my first rental property a week ago and will close end of this month. But I am trying to post ads whereever I can now and hopefully i can get a qualified tenant before closing. But, I am soo nervous now and not so clear what to do on many things and need your help desperatley. Here are my questions

1: Application fee, the question might sound silly, sorry, just want to make sure everything i will do will be right. Should I ask them to mail me a personal check or money order? should I wait till i get the money to do the background check?

2: since we will close the house not until end of March, meaning we are still not the owner yet, do we have the right to sign a leasing contract with the tenant before closing for the house we don't own yet? or, we have to wait till we close it, that way, we might lose the potential
tenant.

3: is it right that we can't cash the deposit check?

Big thx for your help!

Nicole