There's a large sum of info in this thread given by an expert on Chechnya:

http://www.reddit.com/r/AskHistorians/comments/1dxxob/wednesday_ama_chechnya/

Here are some highlights of the thread which may help answer your questions.

This comment chain in specific should answer your question about the First Chechen War: http://www.reddit.com/r/AskHistorians/comments/1dxxob/wednesday_ama_chechnya/c9uw9zc

This comment chain dissects one of the major battles of the First Chechen War for an indepth look at Russian mistakes: http://www.reddit.com/r/AskHistorians/comments/1dxxob/wednesday_ama_chechnya/c9uw906

Tactical Changes in the Second Chechen War: http://www.reddit.com/r/AskHistorians/comments/1dxxob/wednesday_ama_chechnya/c9uwng4

Differences in Attitude Amongst Russian Generals in the Second War: http://www.reddit.com/r/AskHistorians/comments/1dxxob/wednesday_ama_chechnya/c9uyzwx