Hey James, I've never used Tamiya spray cans, but will try to answer some questions for you anyway!
(No compressor - neither do I! But I still airbrush, using the canned air option. I know it's more expensive in the long term, but I generally stick to 1/72 aircraft, and some 1/48 single-engined WW2. Good way to start if you don't want to throw down $ for the compressor right away.)
question 1 - It sounds almost like your later coats have more pigment than the first coats, and this starts to show after the later coats. Are you shaking the cans well? I've also heard of setting a rattle-can in a dish of warm water to help with mixing & flow. A light sanding with really fine sandpaper in between coats would also help.
question 2 - Yes, even a basic airbrush is better than the spray cans. Control control control. Spray cans are on, or off, nothing in between & I've always seen way too much overspray from a can. Overspray = wasted paint & a mess to clean up after. Smoother - should be, but you have to make sure to mix the paint right for your airbrush. Not too difficult, just need some practice.
question 3 - those pro-built models, well, they're built by pros! I suspect you could give some of those guys a spray can & a nail file & they'd be able to turn out something great! How to?? Practice my friend! And if it's smooth you're looking for, don't forget about a clear coat, like Future, which can also help smoothing things out.
question 4 - Removing masking tape - you generally want to remove as son as the last coat of paint is dry enough to be handled. And pull the tape away from the freshly painted area. For a spot like a canopy, you can also use an exacto knife to carefully cut at the edge of your tape line before removing the tape for a crisper line. And don't be afraid to do a little touch-up afterwards if necessary. You can decant a little of the spray-can paint into a small jar, apply it with a brush to the areas that need touchups.
The biggest thing is practice - you say you've got 6 models built right? Those pros we're looking at have built dozens, if not hundreds, of kits - so don't get too discouraged. Hope I've helped,