Decision Trees are actually very easy to provide data to because all they need is a table of data, and which column out of that data what feature (or column) you want to predict on. That data can be discrete or continuous for any feature. Now there are several flavors of decision trees with different support for continuous and discrete values. And they work differently so understanding how each one works can be challenging.
Different decision tree algorithms with comparison of complexity or performance
Depending on the type of algorithm you are interested in it can be hard to find information without reading the actual papers if you want to try and implement it. I've implemented the CART algorithm, and the only option for that was to find the original 200 page book about it. Most of other treatments only discuss ideas like splitting with enough detail, but fail to discuss any other aspect at more than a high level.
As for if they take into account the dependencies between things. I believe it only assumes dependence between each input feature and the prediction feature. If the input was independent from the prediction feature you couldn't use it as a split criteria. But, between other input features I believe they must be independent of each other. I'd have to check the book to ensure that was true or not, but off the top of my head I think that's true.