Q1:  thrust::sequence()

Q2:  thrust::plus()

Q3:  

rbind(c(1,1,2),c(1,0,0),c(0,1,0))

Q4:

library(parallel)

matcumsum <- function(cls,x) {
   rowgrps <- splitIndices(nrow(x),length(cls))
   clusterApply(cls,rowgrps,
      function(onegrp) myx <<- x[onegrp,,drop=FALSE])
   results <- clusterEvalQ(cls,t(apply(myx,1,cumsum)))  
   Reduce(rbind,results)
}

test <- function() {
   x <- rbind(3:5,c(6,2,9),c(5,12,13))
   cls <- makeCluster(2)
   print(matcumsum(cls,x))
}

test()