Normalizing to a higher LUFS (ie going from -28 to -18) is an increase of 10, so yeah, it would be louder. If you have a track that is at -12LUFS and normalize to -23, then it should be lower.
Again, on the drum software, I can't really comment. Havent used that drum system. I'm guessing there's an echo setting somewhere, possibly gated?
Using the Fantom to generate the drum tracks as waves is perfectly fine. My first recordings with my SR18 were generated that way. I had patterns that I "played" and ran the audio out to my Yamaha AW16G. I never really got the Alesis to work with midi, I didn't have the time or the inclination to explore it back then. I also found that I sucked at programming drums.
It shouldn't matter if you are mixing on a different system, as long as you aren't using any of the internal Apollo plugins. I have a main system downstairs for recording running from my Tascam interface. Upstairs, I have my Dell with email, browser, taxes, etc. It also has Reaper. I added a couple of JBL 305s to the regular Realtek internal audio and it works just fine. I've done mixes on this computer just because it was handy. In this case, I don't even have ASIO installed. The ASIO driver it the go-between for your computer and your audio interface.