They are all good choices. I am partial to the 05-08 models because I like the front bumper and fogs better (you could always just swap it down the road).
Going down the list.
1. These cars are actually quite different. Things the LE will have that the CE and S may not include:
Map lights on the mirror
Tweeters in the Front Doors
Time adjustable intermittent wipers
Double center console storage lid
Much softer and more plush seats
Wood Grain Interior Trim
Specific LE wheel covers (if it doesn't have alloy wheels)
195/65/15 Tires (vs. 185/65/15 on the CE)
On the 2005-2008 Models they "ALMOST" always have a 6 disc CD changer
That is most of it.
Things the S will have the CE and LE will not have include:
Body Kit
Fog lights with factory switch in the turn signal stalk
Black interior
Specific S wheel covers (if it doesn't have alloy wheels)
On the 2005-2008 models a lot have the 6 disc CD changer but not as many as the LE
2. Yes it is but it is pretty pricey. You will need an S front and rear bumper, both sets of lips, the side skirts, and all the associated seals and hardware. The body on the S is actually made to accept the side skirts so on the LE they won't be as sturdy unless you drill into the body. It has been done with no issues just supporting it at the front and rear.
3. The gauges from the 2005-2008 will fit but the fuel gauge will not work without swapping out the fuel tanks and the sending unit. This is unfortunate as the Optitron Gauges from the 2005-2008 LE are very nice. However the 2003-2004 LE has a really nice set of white gauges.
Some things that changed on Corollas between 2003-2004 and 2005-2008 include:
Addition of XRS trim for 2005-2006 with the 2ZZGE Engine, 6 Speed Transmission, Rear disc brakes, different gauges, different steering rack, X brace behind reat seats, standard strut brace, and different wheels/tires.
Addition of engine immobilizer
Drive by wire
Different front bumpers
Different tailights (change of the amber turn signal lens to clear)
JBL Sound system
Tire Pressure Monitoring Option
Optitron Gauges
Differnt Fuel Tank and Sending unit
6 Disc CD changer
Removal of Tape Deck in 2005
And I think that is all.
Even though you would like a white car I would stay away from white Corollas. They do not have clear coat and the paint fades and stains extremely easily. This is a common issue on the white Toyotas that are not metallic paints. I like the 2005-2008 based on looks and the drive by wire throttle (less stuff to go wrong) but a lot of people don't like the way the throttle behaves and looks are subjective.
All in all a Corolla is a great car and one with a good service history is hard to come by with a car in this price range. What ever you decide to go with will ultimately be a good choice. Oh and get a 5 Speed

.