In the exact center of the room is usually the best place to start. Make a grid on the floor and ignore any 'offsets' in the layout. And I would lay them out ' dry ' before you set any tile....just to make sure it's gonna look right.
That depends on a few things. I always start at the most visible edge when entering the room. when you enter the room what wall/counter etc are you looking at and the cleanest corner. In a bathroom the tub should be the squares thing in that room. so I start at the most visible corner.this avoids seeing 1/2 or pieces of tile and is neater finish. you see full tiles. Now if you have more than one entry to the room you want to avoid pieces in high traffic walks or at a top of a stairwell my hall has the basement stairwell/dr.(i want full tiles here). This leads to loose broken/chipped tiles after time.make sure you measure first square and true. there's a little planning involved. some like to start in the middle but then you end up w/ pieced tiles all around edges. bad