If you never have disassembled a gun (in particular a handgun), what should one expect when they do it for the first time?
Success.
Should a new gun be disassembled and cleaned/lubricated before firing for the first time?
Generally speaking, yes.
More importantly what should they NOT try to do?
Rush, get ahead of yourself, try to figure it out on your own without the manual, or go "too deep."
What should one look for once the gun disassembled?
For a brand new gun these days you're really just looking at how it works to establish your own knowledge base. There's very little that you're likely to find wrong with a new gun -- that would bother you or that you'd have the knowledge to diagnose. If by chance you see something that's clearly broken, of course that's something for the manufacturer to deal with, but the chances of that are extremely small.
Do you use 'gun grease', gun oil, all-in-one cleaner/lubricant, WD 40, or ???
Use whatever the manufacturer recommends, where they recommend it. Usually that's going to be a "gun oil" of some sort. Like RemOil, or Breakfree CLP, or any of the other common brands.
About how often should a gun be cleaned?
Huge debate there. Some guys are obsessive and will clean the gun every time it is fired. Many others will clean every 500 or 1,000 rounds, or just when they feel like they need to. You should wipe down with an oiled rag any metal surfaces your hands touched, each time.
Is there a difference between servicing one and merely cleaning one? If so then what?
Not really. Most guns live their whole lives without needing any "servicing." Those shooters who actually do put more than a few thousand rounds through their guns will replace the primary springs every 5,000-10,000 rounds generally. You can order those online either from Brownells, Midway, or directly from Wolff Gunsprings. Otherwise, very little will ever need to be serviced unless something breaks.
How much would one expect to spend on cleaning/servicing items?
Not sure what you're asking there. Maybe $10-$15 to get the supplies and brushes to do the job. You need a can of oil, probably a can of powder solvent (like Hoppe's), and either a cleaning rod, patch puller, and brush to fit your bore size, or a universal cleaning kit which will have a variety of brushes, patch-pullers, patch jags, etc. in it. An old t-shirt makes a fine cleaning rag and bore patches.
An old towel, preferably light colored, makes for a fine table-top mat to keep gunk of the kitchen table and to keep small parts from rolling away.
How long should cleaning/service take for the first time?
The first time you do it? Kind of depends on the gun but not more than 1/2 an hour, I'd think.
Can any parts be put back in backwards or wrong?
Depends on the gun, but these days very few guns are not built somewhat "idiot proof."
Most guns (probably ALL guns) have a "field stripping" routine which the manual will explain. How to remove the slide, bolt, barrel, cylinder, trigger group, etc., etc. How to break down the gun into its major assemblies the manufacturer expects you to do yourself and keep clean.
And most (probably ALL) guns should not be stripped down any farther than that by anyone who's not VERY experienced in what they're doing. Going too far with your cleaning job can leave you with a pile of pins, springs, and nearly unidentifiable pieces you'll carry into the local gunsmith in a baggie. That's embarrassing.
When you're buying supplies you'll probably want an aerosol "gun scrubber" or something like that which you can use to blast out the more complicated assemblies to get the gunk out without taking them apart.
