Are you left handed? If you are left handed, and the empty case (shells are for shotguns) ejects rearward and rightward, you'll get hit in the face. Alternatively, your grip and stance need to be adjusted. You may be using an isoceles stance that fails to keep your arms nearly locked out in front. You may also be "limp wristing" the pistol, which will often cause a failure to eject the spent case, but may also eject the case back toward your face.
I had a tendency to flinch and blink when I fired. Should that go away with practice?
Don't do that. Keep your hands relatively relaxed around the grip, contract only the muscles of your trigger finger. Don't anticipate the recoil. Press the trigger rearward until the gun goes bang. Dry fire a lot.
I loading the magazine the right way, by inserting one round at a time and pushing down on the ones already in the magazine? Wouldn't it be easier to have some lever or slide on the outside of the magazine, that would depress the "floor" all the way, thereby making loading easier?
No.
How does this model compare (in terms of size, weight and recoil) to Sig P232 .380?
It's bigger. The ammunition for the G19 is 9x19, 9mm parabellum, or 9mm luger (different names for same round). It has substantially higher muzzle velocity, bullet weight (on average), "stopping power" and muzzle energy. A .380 is also known as the 9mm Kurz (9mm "short"). It's nice for a backup gun, but not as powerful as the 9mm luger.
Of course, I meant as "powerful", relative to the 9mm luger. The 9mm luger is not a particularly powerful round.