I remember learning back in the day that William the Conqueror made all of the aristocrats in England swear an oath of loyalty to him which superseded their oaths to their immediate lords, and that this greatly increased his power. I think I also remember learning that this centralization was a big part of why England became such a military power, and was able to go fuck with France for so long, despite France being so much larger. Is this accurate?
If so, then I'd love to know if it imitated by other monarchs. And when & how did that happen? And if it didn't, then did they find other ways of consolidating their power?
Post hoc ergo propter hoc
In other words, did the swearing of the oath greatly increase William's power, or was William's power displayed by his ability to force the English lords to swear that oath? I would tend towards the latter.
I think I also remember learning that this centralization was a big part of why England became such a military power, and was able to go fuck with France for so long, despite France being so much larger. Is this accurate?
There has been a bit of work done on this point. Essentially, France had more resources but could not mobilize them at any one place and time effectively because of the size of the operation, and England was reversed - fewer resources, more able to put them where they were needed most. See: Philip Contamine, "Warfare in the Middle Ages".
For your last point I wrote up this post comparing and contrasting France and the HRE during the medieval period, which might help you out - let me know if you need more info on that.