I think all your questions were answered somewhere along the line, but let me put it all in one place.
Paragraph #1 --
Yes the amp that's 400w at 4 ohms bridged would theoretically be 200w at 8 ohms bridged, but that's only if it's a good quality amp that doubles its output at 1/2 the impedance. The easier way to tell what it would be at 8 ohms bridged is just combine the 4 ohm stereo power. If it's 400x1 at 4, it could be anywhere from about 100x2 at 4 to 175x2 at 4 so it COULD be anywhere from 200x1 at 8 to 350+.
Paragraph #2 --
It's possible, but the above solution would be better. The stereo operation as mentioned in a previous answer could be a problem.
Paragraph #3 --
300w to a decent quality 225w sub shouldn't be a problem. If things don't sound right you can always reduce the gain a little.
Additional details question #1 --
If you're wiring the coils in series you just run a wire from one of the sub's (+)'s to the opposing (-), and the amp would connect to the remaining (+) and (-). If you're wiring the coils parallel you just run a "jumper" wire from (+) to (+) and (-) to (-) on the sub. Then your speaker lead from the amp connects to one vc or the other -- doesn't matter which.
Question #2 --
No. In this day and age of low impedance high power amps a lot of poorly informed people believe running at a high impedance is ALWAYS bad which is not the case. Running at a higher impedance generally produces less power out of the amp (which is not a bad thing as long as you're still getting adequate power to the subs), but there are a couple factors that are improved by doing it. Damping factor is increased, and THD is usually decreased. These will only make a very slight difference in sound quality, but SQ purists would say it's very advantageous.
Question 3 & 4 --
No - an amp that's 300 at 2 should work fine. If it's 500 or 600w bridged at 4 and you're running it at 8 I think it would work fine. Check the amp's stereo power at 4 ohms to see what it will give you bridged at 8. If it's 400 or 500w you'd want to be very careful with the gain and bass boost.
Keep in mind the only time an amp will actually produce the power it claims is at very high demand points in the music (with a sub amp, the first instant of the BOOOM). Otherwise the power output is very low, and the average output of a 300w amp is only going to be around 100w at HIGH volume. Assuming you're not blasting it the speaker may actually only receive 50w or so on average.