Does anyone want to offer any more information?
Don't take me wrong, p3undone, but you are approaching your selected subjects here in an impatient American way, in the apparent rush to get the quick answers. Unfortunately, this invites shallow answers - even though given in good faith, but it unfortunately does not teach you anything of value. So what do you now know about early Piasts?
You were shortly told about one succesfull and cunning dynasty (of Piasts) taking over power from other families. You were also told of a bunch of semi-legendary predecessors of Mieszko I. And that's more or less it.
But since you never asked about it you were not told about other very important issues:
+ Relationships with Western Slavs, German margraves and Holy Roman emperors
+ Relationships with Czechs and Kievian Rus - winning and loosing control over lesser of greater pieces of land
+ Role of the Church in tempering the ruler's absolutism - as opposed to Byzantine caesaropapism further east
+ Continuous internal power struggle and various revolts. Family feuds: assassinations, exiles, mutiliations, blindings, poisonings ...
+ Continuous alternate regional breakdowns and unifications of Greater Poland and Lesser Poland until the last of Piasts. Complete separation of Silesia, Pomerania and Masovia and subjugation the first two of those provinces to Bohemia and German margraves. (Masovia joined Poland quite late)
I set this thread up so that I can ask specific questions which will draw out insight as well as give me an academic understanding of Polish issues across the board
If you want an academic understanding of basic issues why don't you ask us about good sources for all of this. You already got one such suggestion - Jasienica. I am sure everyone has their own one. I found something concise and readable: Cambridge Concise Histories: A Concise History of Poland, Jerzy Lukowski and Hubert Zawadzki
Available in Chapters.Indigo and Amazon but there is also part of it available online: 30 pages or so, covers Piast Poland, slavia.org/drawsko_history_1.pdf