The outlet arm of the p-trap needs to slope at 1/4" per foot to the next connection. If the water has to flow up to get out of that arm it will accumulate crud in the trap and clog. It probably would drain slowly, which isn't good for a shower, either.
You might want to check out www.johnbridge.com for your tiling questions. They can help you build a shower that both meets codes and will last while giving good service.
You are right to want the drain in the middle of the shower, it looks best and performs best while ensuring you don't end up with sever slopes to the floor.
Ensure you put your liner on a sloped floor, not flat on the floor, or the shower will accumulate moisture in the mudbed. While this technique is used (still), it doesn't meet the national codes and will end up with a swamp under the tile eventually, unless the shower is only used on occasion.