Purchasing the property I’m currently renting

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I’m interested in purchasing a duplex I’m currently renting. It’s in an up and coming neighborhood, the unit next to me has been vacant for months, and their lawn is completely overgrown. I see this as the perfect opportunity to purchase my first deal from the absentee owner but I don’t know where to start!

Should I have the property inspected/appraised?

As a tenant, am I (legally) allowed to? (My biggest question)

When I reach out to the owner should I mention the inspectors findings, if any?

HELP! I live in a fairly competitive market and I don’t want anyone to take advantage of this deal before I can.