1:

ridgelm <- function(xy,s) 
{
   ycol <- ncol(xy)
   a <- cbind(1,xy[,-ycol])
   aas <- t(a) %*% a + diag(s,ycol)
   solve(aas) %*% t(a) %*% xy[,ycol]
}

2:

# arguments:

# rsdf: a data frame in the standard (userID, itemID, rating, covs) format
# idCol: column number in rsdf of the grouping ID, either user or item ID
# dummyCol: dummy variable on which average rating is to be found

# return value:

# copy of rsdf, with an exra column: for a given row (u,i,r,covs), the
# value of the new column will be the mean rating given by user u among
# all rows for which the given dummy is 1

makeAvgCov <- function(rsdf,idCol,dummyCol) {
   dm <- as.numeric(rsdf[,dummyCol])
   rsdf.sub <- rsdf[dm == 1,]
   id <- as.character(rsdf[,idCol])
   id.sub <- as.character(rsdf.sub[,idCol])
   meanNoNA <- function(x) mean(x,na.rm=T)
   tmp <- tapply(rsdf.sub[,3],id.sub,meanNoNA)
   newCol <- tmp[id]
   cbind(rsdf,newCol)
}