Flooring Tile - Ceramic tiles border with Carpet

I am putting ceramic tiles (12") in 7'X2'2" area near the entrance in the basement with 1/4" spacing between tiles. Currently the whole area is covered with the carpet. I will first trim the carpet in this area and then put tiles over the concrete floor.

Questions:
---------------
1. Both carpet and tiles top are coming on the same level. so I think I won't need anything in between them for smooth transition. Should I put the last tile row at the border of the carpet or should I leave some space in between (1/4" may be)? If I leave the space then what should I put there? Grout or some caulking?
2. Should I start the tiles at the edge of the wall on the other side or leave 1/4" space for grout between wall and the tiles?

but the tile up to the edge of the carpet and tuck the carpet to the tile edge.On the other side remove the baseboard and leave a small gap between the wall and the last tile do not grout ,put the base back on and if you want you caulk the tile to the base or leave it alone:cool: