How to prove to my landlord that bitcoin came from my wallet?
One way might be to have the landlord generate a different address for each tenant. So you pay your landlord using address A, and your neighbour pays using address B, and the landlord can tell who the payment came from by the destination address.

That doesn't prove that the payment came from your wallet of course, but this allows somebody else to make the rent payment on your behalf (and the landlord wouldn't know the difference).