Translation:I walk to my house.
To indicate the extent of doing something, either by time, distance, etc. This means the speaker will walk just until he/she reaches the house.
★ まで - until, as far as, up to
Until [I reach the] house, [i (will)] walk.
Uchi is home, ie is house http://yesjapan.com/YJ6/question/2752/what-is-the-difference-between-uchi-and-ie
Yes, or it could use the particle へ.
Let's see if this makes sense: - に puts emphasis on the destination (like "Ugh, I'm going home" when you're done with work and can't wait to relax) - へ puts emphasis on the travel (like "I'm flying back home" to indicate you're dealing with the hassle of air travel) - まで contrasts with から to put emphasis on how you've come from somewhere to arrive at your destination (like "I've just been released from jail and I finally get to go home again.")
I'm a non-native speaker, so I could be a little off on some of those, but hopefully that helps some....