I'd remove the starter and then push-start it to see if the grinding continues. If it does, you know it's the starter.
Yes a '99 AX-15 transmission is the same as a '98 AX-15 transmission. If both were behind a 4.0L engine, both are the AX-15. The manual transmission behind the 2.5L four-banger is the AX-5 and it is not interchangeable.