The answer to half of your questions: Beer. Beer is a massive part of Czech culture. Our media is not great, there are not a lot of good czech films or songs. Try to avoid small bars or sketchy looking restaurants, quite a lot of Czechs are xenophobic, mostly in these bars where 50-60 year old Czechs go to hang out. Definitely visit a brewery and a castle (a good choice would be "karlštejn"). There are many good Czech books, a great example would be "Babička" by Božena Němcová (one of the most important authors of our country, she is on the 500kč banknote). Other notable authors are: Karel Čapek and Jan Neruda. I don't particularly enjoy books by these authors, regardless they are an important part of Czech literature.

Hopefully that's enough for you, if you are visiting the Czech Republic: I hope you have a nice time here.