Hi, I am interested in extracting expression data for only three cancer types from GSE62944. I want tumor/normal integer based read counts for these cancers, from which I want to extract Differential expressed genes using LIMMA. Is it possible to do so? I am not able to understand which samples belong to which tumor types and how to extract them. Also, can it directly feed the feature counts data to LIMMA for differential expression?

Have you read the vignette? https://github.com/Bioconductor/GSE62944/blob/master/vignettes/GSE62944.Rmd

There is an example on subsetting data for Low Grade Glioma (LGG), which you can easily modify for other cancer types.

# metadata on cancer types
phenoData(tcga_data)$CancerType

# subset the expression Set to only samples from LGG for example
lgg_data <- tcga_data[, which(phenoData(tcga_data)$CancerType=="LGG")]

The example continues with differential expression analysis using DESeq2, but you can also use limma. Check the following workflow on using limma for RNASeq: 

source("http://bioconductor.org/workflows.R")
workflowInstall("RNAseq123")

Hope this helps!