Thanks for the title change

A few observations...
1. On Initial, although the way you have your vlookup, is working, the search criteria really should be a single cell...
instead of...
=VLOOKUP($A$2:$A$5,'Sheet 1'!$A$2:$C$32,3,FALSE)
rather use...
=VLOOKUP($A2,'Sheet 1'!$A$2:$C$32,3,FALSE)
copied down

2. On sheet2 col Q&R, you are searching in a range that already contains the criteria. Realistically, you should have a criteria in 1 cell, and search for that in a totally different range - else why even bother to search for it?
MATCH('Sheet 2'!J3,'Sheet 2'!$J$2:$J$5,0)
You are searching for J3 in the range J2:J5, so it will always return the same relative row number

Which sheet gets the new data with each update, and which sheets go and fetch/reference parts of that update?