1 or 2 Subs

First thing Phatguy.  Get rid of those sony's. Kenwood's a good brand, but they've (just like everyone elso though) have had some problems w/ their hu and amps.  Pioneer is a nice brand, in my opinion, better then Kenwood.  Second thing name a price range for your system.  I (and anyeone else here) can give you a $300 system or a $10000 system.  It's all up to you.  Out of the two subs definately go for the Pioneer.  They have some good stuff.  Also look into JBL.  To answer the question of control for a sub think of it this way:  which is easier to move? a 100 lb guy or a 150 lb guy?  Obviously the 100 lb guy is and so is a 10" sub.  But then I've herd some 12" subs that sound better than a 10".  Two 10" subs will normally sound "louder" than a single 12" but once again that can change.  I would go w/ one ten and possibly upgrade from there.  I'm a fan of JL, Kicker, and Infinity.  The latter is probably your cheapest, and the first two being some higher-end speakers/amps.  With a corolla probably set the sub in back (the trunk) and aim it toward your license plate.  Trunks are normally sealed and soundwaves have a tendency to just bounce around.  When you face it toward the front of the car you let the subs reflect off the back seat and then to the back of the car where they then reflect off of the back of the trunk and go toward the front.  This is why some systems set up like that sound louder when the trunk is open.  As far as box type,  you want control so go with a sealed.  I'm not sure what you mean with the amps but as far as crossover most mono sub amps have a lowpass crossover built into it.  As for your normal speakers use your hu to keep the heavy bass of of them.  Let the sub do the job.  Look into an amp that has a remote input that allows you to turn up the bass when you want it to boom.

For better specs on the Kenwoods:  http://www.cardomain.com/item/KENW25092PAK

http://www.cardomain.com/item/KENW30092PAK

Im going to take your word for it and go on the premise that you cannot get your hands on anything else but what you have listed.  That said, here is my opinion.  You need to post RMS power ratings for the amps you listed.  RMS into 4 channels and rms bridged. 

If you can go with 2 12's then i would in this case rather then 2 10's.  The power handling is not an issue, 12's rarely handle a meaningful amount of power over 10's of the same model line.  In this case the 10" kenwoods handle 350 and the 12's 400.  If it comes down to the 10's I say either or, but i would choose the pioneer for reputation and brand alone (neither is substantially better then the other).

The enclosure will partially dictate how much power the sub can take.  Sealed boxes tend to take more power to reach the same SPL as a ported.  If you port you must do it properly.  Whatever speaker you choose should come with several enclosure designs.  Pick one of those, the actual shape of the enclosure do not mater, so long as the proper airspace is contained within.  So, design the enclosure to fit your car with the help of the calculators on this site.  Subtract the port  and subwoofer displacement from your airspace number.  Build said enclosure.  Add subwoofers.  Pour out some liquor for the dead homies.  Your in business.

Ya know I don’t bag on most of Sony's products as hard as others.  Now the Sony Xplode stuff is never my first choice, but its usable and better then a dozen brands that shall remain nameless.

The speaker should move if your talking about the woofer part of a full range speaker.  The size of the speaker and the power applied will determine your crossover spot.  For example a typical 6.5" full range speaker, power to its rms rating (not over) will typically like the crossover set around 80-100hz with a 12db slope.  You want the cone to move as much as possible to get texture and depth to sounds like the male human voice.  But if your cone is popping from bass, you should probably turn the crossover up, or check the power you are putting to the speaker.  If you have a variable crossover then you can turn off the sub and mess around with the crossover to hear the difference it makes on your music.

Thats enough for now, send pictures of your pimped out corolla.