Welcome back to the hobby and welcome to the forum! I'll try to answer your questions individually. Keep in mind that there is probably no single or correct answer to any of your questions, but rather, multiple answers, and everyone does what he likes best, what works best for him.
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Do I need to clean/de-grease modern model kits before painting? Some say yes, but they seem to be old-schoolers that have done it that way forever. Other's say modern models do not require it.
It's not a bad idea, but it's personal preference. The object is to remove anything like mold release compounds, grease, oil, dirt, and start with bare styrene. I do wash kit sprues before I start assembly. I use an old glass baking dish, add warm water, and a couple drops of a de-greaser (SuperClean). Others will say that they don't bother cleaning the parts, and have never had any problem. I prefer to do it.
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Do you use primer on the model? My thoughts are that every layer of paint will degrade the ability to see details molded into the model, so the less layers of paint the better.
Priming is intended to improve the adhesion of your color or finish coats of paint. It also can serve as a quality control step-a coat of primer can highlight flaws that you didn't see, like seams that still need filling, scratches or other marring on the surface, things that can ruin your finish coats and make some remedy necessary. That might be as simple as touching up of the blemish, or as drastic as stripping the color coats and staring over.
Again, some say they don't prime, but I think more of us do. I do. I like Tamiya's Fine Surface Primer, though I have also used Rustoleum's primers and Walmart's house brand automotive primer. The last few cans of both of those products wound up clogging badly, though, so I haven't used them in over a year.
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Do you paint the parts while they are on the sprue, and then paint again after cleaning up the marks left from cutting the part, or do you cut the part from the sprue and sand the marks before painting? Cutting and painting small parts seems would be very difficult when not on the sprue.
Again, everyone will have a preference. I'll paint some things on the sprue, especially small parts, if I might lose them if I remove them first. The drawback to painting on the sprue, in my opinion, is that I probably will have to go back and touch up the sprue gate on the part after I install it on the model. Personal preference.
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Does modern modeling glue chew-up the paint and not adhere to the parts like they used to? I have super-thin modeling glue that I got because the reviews of the Tamiya kits say that the parts fit really tight requiring super thin glue delivered with what amounts to a needle. That's fine if it doesn't ruin the paint around the edge of the parts.
If you mean, will styrene glue damage paint? Yes. Does paint on the surface interfere with the glue? Yes. That's why we have the old tip to scrape away paint from mating surfaces before applying glue, for a better bond. Does everyone do it? No. I do, though.
Also, I prefer to use styrene cement to attach styrene to styrene. I like the idea of the weld between two parts. CA glue does not create that bond, so I don't use it to assemble my models. Except to attach unlike materials, like PE, resin, or metal, to styrene. On my resin builds, or metal figures, I'll use 2-part epoxy for most assembly, because I think the bond is stronger over time than the bond CA glue provides.
I use Tamiya super-thin, as well as Testor's in the black plastic pentagonal bottle with the long spout. I have used Plastruct's Weldene and Bondene, when I started working with liquid glues. They're good, and I'd still use them, but I do like Tamiya's flow.
And I still use good ol' Testor's tube glue for some applications, strings and all.
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Related to the last, do you glue the small parts to the main part and then paint, or do you paint and then glue? It seems to me that the former would just create obstacles to paint around when painting the larger part's details.
This question is also related to your question about painting parts on the sprue. I'll attach parts then paint or paint then attach, depending on how difficult or even impossible it would be to reach that part. Painting a car dashboard, for example-probably can't paint it once it's installed, so, I'll paint it first, then install it. Or pieces of equipment on a figure. I'll attach something if I can still get to it and if it doesn't prevent me reaching something else.
Again, there will be different opinions.
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If the parts do not fit that well, how do you address the gap(s)?
Again, several ways, and personal preferences.
For gaps-proper, open gaping gaps between parts, I'll use putty, like the old Squadron white-not their later, more recent variety. I thin it with acetone to liquefy it and use an old paint brush to apply it. I'll also use a cotton swab soaked in acetone to remove the excess and minimize the amount of sanding and resultant damage to the surrounding area. You have to be careful with the solvent-it's "hot" and can damage the styrene. But very small amounts are all it takes.
Or I've even used 2-part epoxy putty, which I use on metal and resin figures, and for sculpting. I like Aves ("ay-vees", Latin for "birds"-I know, I asked 'em), personally, but there are many brands.
Or I'll use styrene scrap, whether pieces of styrene sheet, or sprue, stretched or not, and then flow liquid styrene cement over the filler. Once the glue has cured, then I can cut, scrap, sand away the excess.
For seams-fine separations, not big gaps-I like to use the "squeeze" technique and reduce the possibility of visible seams at the start. This works well on long seams like along aircraft fuselages, or around the edge of wing top and bottom halves, anywhere you can apply a little pressure along the seam. You hold the pieces together, flow liquid styrene cement along the join area, and apply pressure. A little bead of melted plastic will extrude. When this cures, you can scrape away that bead with the back of a knife blade, and then finish with fine sanding as necessary.
Failing that, I'll use the putty and acetone to fill the seam, or even pieces of stretched kit sprue and liquid styrene cement. When it's dry or cured, then I sand as necessary.
As far as sources of tips go, besides this forum, where you'll find other answers to your questions in some of the other subforums, too, I still like Shep Paine's classic books. I happened to pull out "How to Build Dioramas" again the other night and read it. His advice still holds up today.
The big thing is your own experience, though. Get building, try things, see what works for you and what doesn't. In the end, that's really the best way.
I hope this all helps!
Best regards,
Brad