Purchased with Cash. When can I refinance?

[Account Closed]

1) How long do you have to wait before you can refinance a property after buying with cash/HELOC?

2) Do you get the same interest rates or worse than if you had just financed at the start? 

3) Is there a term for when you re-finance a purchased home? i.e. is this a cash out refinance?

Plan

- Buy home with HELOC (aka cash) for better deal hopefully.

- Refinance property 80% LTV into a 30-year fixed and pay off majority of HELOC.