When can LL Start Showing Apartment?

[Parakeeta Byrd]

I advised my landlord that I will not be renewing my lease, which expires on May 31, 2015.  I have two question:

1.  When can my landlord start showing my apartment to potential renters?  A month before end of lease? Two months?  I want to cooperate, but I really don't want someone popping by in, say, March.

2.  As my lease expires on May 31, does that mean I need to vacate on that date?  The problem I'm having in my new apartment isn't available until June 1, so I'd like to arrange for a mover very early morning on June 1.

I've been a very good tenant and want to be cooperative.

I appreciate any advice,