Does my 2005 Mazda 3 have a timing chain that needs attention at 90000 miles

Only timing belts require replacing your mazda has a chain that is service free.If the car is running ok then leave it be.

According to Mazda it is a chain.
It is an automatic? You should be on at least your second Transmission fluid change.
Power steering fluid - Most of the time it is just ignored but some people use a turkey baster to **** fluid out of the reservoir and then refill. Doing this several times a year is better than nothing.
Oils can be dumped at Checker/Autozone..
Radiator fluid. You should be on your second time for this too. Do it yourself for less than $10 or pay $80. Disposal of old fluid is not easy.
If you do the brakes yourself, do you ever flush the brake fluid? A bottle of fluid is $5 - a mechanic will charge you $100. You can do it yourself (with the aid of a helper to push the brake). Disposing brake fluid is not simple.
Brake and Radiator fluid have to go to hazardous waste disposal. My city has a few events each year.
You can google these topics and get details (write ups, pics, videos) on other sites. Try and find one that specializes in Mazda 3's. I have a maxima and maxima.org has saved me thousands of dollars.