'However, if you date the broadside era from the 15th century, you're already talking earlier than the period most of us think: I think of it as the 18th and 19th centuries.'
Admittedly there weren't very many ballads printed in the late 15th or the 16th century, but it really took off in the 17th. Strangely we have lots of readily available examples from the 16th and 19th centuries, Pepys, Roxburghe, Bodleian, Madden to name but a few, but the 18th century examples mostly still languish in libraries due to their physical properties.

'As for the flowering coinciding with the advent of print, why would print have helped the development of ballads among the overwhelmingly illiterate lower classes?'
That's the point, it didn't. These earlier ballads only eventually filtered (I hesitate to use the word 'down') to the folk as they were reprinted in later centuries in most cases. These are of course generalisations and there are always exceptions.

'Are ballads more closely associated with the gentry?' To an extent, but also the rising middle classes like tradesmen and the guild members.

'What sort of songs would the people have sung prior to the flowering of ballads, and how would these songs have differed from what we consider a ballad?'
Obviously we have very little evidence of what the people sang. If we base it on what exists today, those homely little ditties, drinking songs, catalogue songs, songs about domestic issues, songs like the Bothy ballads, comic songs. Personally I'm not sure there would have been many ballads as we think of them today, but I do realise I am perhaps in a minority on this one. What manuscripts have survived are obviously from very literate people,e.g., The Percy Folio Mss.

'Might the ballads appear to be "flowering" only because more traces of them are left, or is a different aspect of development meant by the term?' Possibly. It would take a lot of searching to verify any of this.

'It seems to me that print and the broadside industry may have had the opposite effect: that of condensing ballads into shorter, pithier commodities, more easily learned by anyone (rather than the village singer with a gifted memory). The older broadsides tend to be quite lengthy, which would seem to reflect common practice rather than an innovative fashion enabled by print.'
That is the general direction of broadside ballad remaking over the centuries. To what extent this is down to fashion or the movement to a different market is not easy to say, perhaps both. Undoubtedly those broadside ballads that were rewritten for different markets invariably got shorter as they came down the centuries. And usually even shorter once they got into oral tradition. As my belief is mainly that they originated as broadsides or theatrical pieces I don't accept that many of them originated in oral tradition, but you may be right and everyone is entitled to their own opinion on this one.

'Even being able to date events doesn't firmly fix the origins of songs, since history tends to repeat itself with alarming regularity.'
I wouldn't deny this in some cases. Some of the Robin Hood stories were originally about other legendary outlaws before they were attached to RH. However I don't know of any songs about say Napoleon that are based on earlier songs. We look here at probabilities rather than concrete facts. A detailed ballad about say Battle of Sheriffmuir is unlikely to have been about an earlier battle, on the other hand 'The London Man O' War' ballad was actually about a ship called the Nottingham in 1746 and we know the Captain himself wrote it.
Of course love songs and fictional songs, yes, have been written and rewritten over and over, mainly by broadside hacks trying to earn that last shilling and desperate for something to sell the printer.
You can quite easily nowadays find about 95% of the folk ballads common to Eng/Ire/Sc/America etc on broadsides. Not so many of the more local traditional songs, but the general corpus.

Regarding patchwork knowledge. Mine is still patchwork to a degree and I started out as an interested singer, still am. Those songs that looked as though they might be based on facts like shipwrecks, disasters, murders, suicides, inspired me to go and look.