Here is what I was able to do with the 98 & 99 jerseys --

The second is purported to be a 1998 Mets white home jersey. The manufacturer is Russell Athletic and there is a cloth wash tag and a Diamond Collection logo with size 52 and a white plastic-like tag attached and showing below the cloth tag which reads 100% Polyester.
The 1998 Mets white home jerseys were AIS; the white alternates were Russell. Assuming that this is an alternate? Also, would need to confirm that Benny’s size was in fact 52.

The number 39 appears on the left front breast and on the back, unlike the more customary number 50 used for most of Agbayani's career.
Correct. Benny wore 39 in 1998.

Benny may have also worn this jersey in 1999
No, he only wore #50 in 1999.

Both the New York and number on the front and Agbayani and the number on the back are blue/orange/black
Correct. The Mets switched from blue/orange/white to blue/orange/black this year.

with the blue portion having a diamond shaped ribbing texture like in 1999.
Correct. This lettering debuted in 1997 and has been on every Mets jersey since.

The Mets in front is in blue/orange/black script with no line below the team name.
Correct.

There is a velcro strip on the inside of the button line on the front in place of a button.
Correct.

There is a round Mets ball/skyline logo on the left sleeve which seems to be authentic, including the trademark R in a circle near the 4 o'clock position of the sphere.
Cannot tell without seeing.

There is no neck-to-sleeve trim running along the shoulder down to the arms.
Again, this stopped in 1992.

There is an embroidered blue R on the right sleeve. Are there any other characteristics I should check out?
I would also need to see the jersey to determine if lettering (font, size, etc.) is correct.

I would have asked about blue piping, but see that you included that in your follow-up statement.




The third is another Agbayani jersey which I believe is a 1999 Mets alternate road black knit Benny Agbayani jersey. The manufacturer is Russell Athletic and there is a cloth wash tag and a Diamond Collection logo with size 52 and a white plastic-like tag attached and showing below the cloth tag which reads 100% Polyester.
Correct.

Is Russell Athletic the correct manufacturer?
Yes.

The number 50 appears on the left front breast and on the back.
Correct.

Both the New York and number on the front and Agbayani and the number on the back are blue/white/orange with the blue portion having a diamond shaped ribbing texture.
Correct.

The New York is in an old style lettering and not in script.
Correct.

There is a velcro strip on the inside of the button line on the front in place of a button.
Good.

There is a round Mets ball/skyline logo on the left sleeve and the skyline is in black, rather than the usual blue.
Sounds right. Need you to confirm that the border of the patch is blue and not traditional orange.

However, there also is no trademark R in a circle around 4 o'clock in the white field of the sphere as it is in most of the logo patches I have seen.
Would have to check against a photo of a similar jersey of this time.

There is no neck-to-sleeve trim running along the shoulder down to the arms as other Mets uniforms may have had.
There wouldn’t be; however, there should be blue piping. Looks like you covered it too with your additional info.