How come delicatessen offer meat sandwiches AND cheesecakes as deserts? Were people mixing meat & dairy in eastern european communities ? Or were they not really part of traditional ashkenazi food ?
Just because something is called a "delicatessen" and serves traditional Eastern European fare does not mean that the restaurant and its food conforms to the ritual and dietary standards of Kosher laws. Under these laws, meat and dairy are consumed separately and a restaurant, if it wanted to have rabbinical supervision, would have to serve one or the other.
Do you have a particular restaurant in mind? Those with reputable and accepted external supervising agencies would sell EITHER traditional meat dishes (the corned beef on rye, the kishke, the stuffed cabbage etc) or traditional dairy dishes (blintzes). These foods are traditional to Eastern Europe and may also be found at non-kosher restaurants that cater to people interested in that food.
Here are a couple of websites that might provide other information for your learning:
Info about supervision http://www.myjewishlearning.com/ask_the_expert/at/Ask_the_Expert_Hashgacha.shtml
and here is a wikipedia page which gives some good information about kosher vs. kosher style