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The MAF is in front of and above the radiator, where the air filter box ends. The MAF couples on the outlet side to the bridge (with the logo) then the accordian coupler, which on your car was replaced with a smooth coupler. From your pictures it is not possible to tell if you have a Z filter box. Enjoy your car.
Actually what you show in the picture is not the MAF, it is just the housing for the MAF. The MAF itself is black and is only about 3/4" thick. I goes in between the two pieces in your picture.
You can tell the difference between a Z06 airbox and what was stock on yours by looking at the top of the airbox. The stock '98 is solid, whereas the Z06 will have a NACA style duct on top about 6 " wide. If it does have a duct on it, but it is not 6" wide, it is the stock airbox off of a '01 and up corvette.
Looks like they replaced the MAF "ends" with the oversize ones that were popular a few years back. Basically, you just take the mAF apart into three pieces. The actual MAF is the center piece (not in your photo). then you toss the front aluminum piece with the screen, and toss the rear aluminum piece with the little fins inside. You replace these two pieces with opened-up plastic or metal "ends" which give much greater air flow. Sandwich the MAF back in between these new "ends" and bolt it back together.
I think Breathless Performance usd to sell a set - might check their website for a photo/description.
This worked OK apparantly on the early C5's because it passed more air, and tricked the mAF into leaning out the mix a bit.
If you have any surging at part throttle, or ping, then this is the culprit.
If it runs well, just enjoy; it may be good for 5 hp if you were a bit rich to begin with.