Is the Shimano 2303 crank arm and the 2300 crank arm the same? I bought a Shimano 2303 crankset (52/42/34 triple) by mistake although I should have bought a 2300 crank

If I remove the inner 34t, will it have the same structure as 2300 crank? By structure I mean things like chain line.

According to the Shimano manual, 2300 should use 110mm B.B. and 2303 113mm B.B. while the chain line is 43.5mm(2300) and 45mm(2303).

After the separation of the smallest chainring, if I use a 110mm square bottom bracket, would I have 43.5mm chain line?

I'm worried because I'm using a road front derailleur and a road STI lever.
Not a specialist on this, but I assume that the 2303 (being a triple crankset) would have the chainline aligned to have the middle ring right on the center of the cassette, while the 2300 would probably have middle of the two chainrings in line with the cassette. You could probably get bottom bracket with a shorter spindle to move the two remaining chainrings closer to the frame to make things line up perfectly. Be careful that the chainrings and crank arm do not contact or rub on the chainstay when using a shorter bottom bracket. 

As far as your levers go, you will probably be fine, as both the 2300 and 2303 are build for road shifters, and there's no different between road and mountain groupsets anyway in the 2300 level of components. For instance, my bike uses 2300 shifters with a deore rear derailleur.