How to find correlation between two specific genes in same dataset?
I suppose in an idealized world you'd use something like salmon to get TPMs, which can account for differences in effective gene length by sample. However that's quite likely to be overkill.
Not necessary, you're using a with-sample ratio, which wouldn't be changed by normalization.


Here is a small example in R, assuming your matrix or data frame is named m:

first = which(row.names(m) == "ESCO1")
second = which(row.names(m) == "ESCO2")
plot(m[first,], m[second,])


or cor(m[first, ], m[second,]). You'll want a rank-based correlation.