then this about Chechen rebel forces
Russian soldiers met fierce resistance from Chechen rebel fighters intimately familiar with the city, which was transformed into a fortress city under the leadership of field commander Aslambek Ismailov. Grozny's Chechen defenders built a system of bunkers behind apartment buildings, laid land mines throughout the city, placed snipers on rooftops, and withstood the heavy Russian bombardment for the chance to come to grips with the enemy in an environment of their choosing.
The rebels spent an effort on digging trenches and antitank ditches for the city's defense. Chechen fighters used the trenches to move between houses and as sniper positions, attacking the Russians as they focused on the tops of buildings or on windows. The first-story windows and doors were boarded up or mined, making it impossible to simply walk into a building.
Chechen fighters used the weather conditions to step up attacks on federal troops. Well-organized bands of no more than 15 rebel fighters moved freely about the city, often sneaking behind Russian lines and attacking unsuspecting soldiers from the rear. The impressive mobility of the Chechen force included escape routes from interconnected firing positions and use of the sewer network to move about the city; they stated that they did not use body armor because it slowed them down.
Really rather depends on which 'war' you are talking about. In the first Chechen war , the Chechens employed the 'defenceless defence' theory, holding ground for as long as it took the lumbering Russian Army to gear up and go after them, then melting away to attack at another spot. The later war saw the Chechens attempt to match the Russians in a slugfest of epic proportions, hence the unbelievable destruction which ensued from relatively small scale ops. The Second Chechen War saw the rebirth of the Russian shturm detachments, hunting small groups of rebels within built up areas like Groznyj with devestating (for the infrastructure) effect. In comparison to the First war, it was a world away. The Russians had relied almost exclusively on their Cold War doctrine for that show, involving massive use of tanks and artillery which were soon worn down by bands of determined rebels. Their coordination of ground and air assets was much improved from the '94 debacle. Despite this, it was probably a failure by the Russians to ensure that BUAs were properly sealed off before attacks went in which allowed the rebel forces to survive.
Absolutely. Chechen hit and run tactics outside the city caused huge confusion and really savaged morale. This was due to the haphazard Russian 'cordon and search' methodology and also because of how difficult it was for them to distinguish Joe Civvy from Joe terrorist.