Hey, Ayche, welcome to the airgun nut house :-)! I'll run through your questions in order, the add any additional info I think might help.
1. Same action and power, far as I know the Big Cat is about the same as the current Shadow Sport, has a polymer barrel with sleeve. Not sure why the cocking effort is different.
2. Midway is a very reputable company, I bought my first adult air rifle, a CFX, from them, as well as an RWS 350.
3. Doubtful, GamoUSA does what they want, when they want. They told us last year, no more Gamo .22 air rifles. Then all of a sudden, we have the CFX, a gun NEVER imported into the US in .22, available from Pyramyd. Go figure!
4. Not a clue.
5. Depends on the brand, model, and gun. Most .22 scopes are parallax free at 50 yards, even if the scope will handle the air rifle recoil, that's a strech for best accuracy. Most airgunners use adjustable objective scopes that are air gun rated. Pick your price point, there are probably at least a half dozen choices available.
6. Not sure about this, I think Accushot by Leapers has see through mounts for 11 mm rails. They make a good mount at a good price. Check their web site, Leapers.com, for more info. That's the only possible see through I can think of. Other good mounts are BKLs, Beeman, and B-Square, all much more expensive.
Of the rifles you are considering, I'd throw the Whisper out of consideration, in my opinion it's a marketing gimmick. Springers just aren't that noisy, and a shroud, baffle, whatever you want to call it just isn't going to make that much difference. They can seem really loud when you shoot them, but stand back 10 or 15 yards, and you'll see what I mean.
The Big Cat I have no experience with. The Shadow (old Shadow 1000, not new Shadow Sport) I've shot a lot, excellent rifle. Light, accurate, powerful, and not too hold sensitive. The CFX is also an excellent rifle, that was my first in .177, and I just got one in .22. Also light, accurate, and powerful, and not hold sensitive at all. For a beginner, it's perhaps one of the easiest springers to get started with. Because of the fixed barrel, some consider the CFX more accurate than the Shadow, if so, the difference is miniscule. The Shadow may have a slight edge in power, again the diff is tiny. The only downside to the CFX is the rotary breech, it can make loading a bit of a hassle until you figure out a technique that works for you. You also need to think about scope length, too long will get in the way of loading. I found 14 .5" to be max, depending on eye relief, shorter being better. I'd say if you're primary use is hunting, get the Shadow. A fast second shot is much easier with a break barrel. For targets, especially if you're lazy like me and shoot off a bench, I'd go for the CFX.
For caliber, a general rule of thumb is .177 for feathers, .22 for fur. That's VERY general, check out the Hunting gate if you haven't already. Look for posts by Shadow and/or LongIslandHunter. I'm pretty sure either of those two could hunt elephants with their air rifles, if they wanted to :-)! Shot placement is a lot more important than caliber, that and knowing the capability of you and your rifle. Do your part, and either one will be more than adequate for squirrel size game out to 40 yards or so. If you're thinking racoon size, you might want to concentrate on .22, and still cut the range down. Jeff and Ed, do you guys agree, or am I out to lunch again :-)? You won't see that much increase in power between a .177 and a .22 CFX. The .177 will be around 14 fpe, the .22 maybe 17 or so. To get big numbers, you either need a magnum springer like the RWS 350, or a PCP. .177 is flatter shooting, and there are a lot more choices in pellets. .22 gets you a little more power, a loopier trajectory, and not so many pellet choices.
One last thing. Both the CFX and Shadow have synthetic stocks with hollow butts. Adding some weight to the butt can really improve both the balance and general shootability of either one. I like to put a pound of Duct Seal in mine. In case you're not familiar with it, Duct Seal is used by electricians to seal electrical raceways, it's kind of like sticky modeling clay. Most any big box store will handle it. If you prefer a wood stock, go with Vinces' suggestion, the Hunter 440 is a steal at that price, and it also shares the same powerplant as the Shadow and CFX. For the price, that's probably the best deal around right now. You still need a scope, but the scopes on the combos aren't that great, you'd probably be better off buying glass seperately. The CFX .22 is currently only available as a combo with a fixed 4x scope. Not a bad scope, but no where near as much glass as one of these can use. If you go Gamo, make sure you order a trigger from Charlie Da Tuna. Best $32 you'll spend on damn near anything!
Guess that's it for now, sorry if I got too long winded, I tend to do that occasionally ( Dano, I heard that!). If you have any more questions, you know where to come. Good luck, and keep us posted.
Dave