Also, my fiance just purchased a diamond with the following GIA report details.

shape. round
measurements. 6.20-6.27 x 3.76mm
weight. 0.88 carat
depth. 60.3%
girdle. thin to medium, faceted
culet. none
polish. very good
symmetry. very good
clarity grade. internally flawless
color grade. f
flourescence. none

I asked for the Sarin results also:
diam. 6.24mm (6.19 - 6.27)
depth. 3.77mm 60.4%
crown. 34.2' 14.7% 0
pavil. 41.0' 43.3% 0
table. 3.54mm 57% 0
culet. 0.6% ver. small 0
girdle. 0.9thin - 1.4medium 1.1% 0

I have two questions about this diamond. Should the tiny discrepancies in numbers between the two reports concern me at all? What are the zeros at the end of the Sarin report lines for?

Small differences between GIA and Sarin report are ok and due to measurement errors of the machines.

The measurements for your diamond are very sweet - 1.7 HCA - within Tolkowsky ideal range.