Question: When we say "**I am wearing a Tshirt**" (might last a day), we mean "**I have that Tshirt on my body**"

When we don't say "**I am wearing a Tshirt**" to mean "**I am putting on a Tshirt**" (which might last 1 or 2 minutes).

Does "**I am renting a house**" mean I am negotiating with the landlord now (which might last many hours or many days)?

Does "**I am renting a house**" mean I signed the contract already and am living in the house and paying rent monthly now (which might last many months or years)?

Answer: 
"I am renting a house" would generally mean you have completed the negotiations and have a contract, whether you are actually moved in is a bit more questionable though in most cases could safely be assumed. This is from a western US perspective, I suppose this could vary by location.
"I am renting a house / a room" -> that negotiations and contracts are all done would be the most common interpretation.

To mean on-going negotiation, you could say "I am trying to rent a house". And "There's a house I'm trying to rent" would be more unambiguous.