Stuggles with Leopard

I've had my mac for about 2 years and just started to have some software problems. Spotlight is failing big time. Sometimes it's semi functional but when I want to browse my applications, it fails every time. I've installed the new adobe 11 or whatever it is and every time I try to watch a video or go on a website it says I need the new adobe...well I have it and apparently it doesn't work? One more problem. I just bought and external HD to back it up since it seems to be having such a struggle. Time machine doesn't seem to want to back it up. It starts to and then fails part way through. Just says there was a problem or something, no error code. I was just wondering if someone had some advice to help me get my machine backed up and tuned again! Thanks!