Performance issues in for loop (moving towards vectorization with multiple sample()'s)

Question 1

Below is how you would do the first part using data.table, adding CustomerID to the Transactions table. I have changed some names and dropped the placeholder columns as they will be added through the data.table joins.

Tr <- data.table(Transactions)
Tr[, CustomerID:=NULL]
Tr[, ProductID:=NULL]
Tr[, ReferredBy:=NULL]  ## see @Arun's comment for a more compact way to do this

Cs <- data.table(Customers)
setnames(Cs, 'ID', 'CustomerID')  ## So we avoid duplicate with Tr

## Add customer ID, matching customer types
setkey(Tr, CustomerType)
setkey(Cs, CustomerType)

# Make an index Transaction ID -> Customer ID
# Large interim matrix should not be formed, but I am not sure
TrID2CustID <- Cs[Tr, allow.cartesian=T][, list(CustomerID=sample(CustomerID, 1)), by=ID]
setkey(TrID2CustID, ID)
setkey(Tr, ID)
Tr <- Tr[TrID2CustID]

There is a large matrix that is the cartesian product of your Transactions and Customers tables (about 15M rows) which would exhaust the memory if it is explicitly computed. Judging by the fact that this takes about a second, I'd say it is not computed, but I am not sure.

I will work on the rest and edit the answer if I come up with the solutions quickly, but this ought to show you how to do this using data.table.

UPDATE 1: adding ReferredBy

Since the referral probabilities only vary by CustomerType, you can generate the referrals in blocks with replacement (much faster than by individual ID)

setkey(Tr, CustomerType)
Tr[, ReferredBy:=sample(ReferredByOptions, replace=TRUE, size=.N,
                        prob=c(BySearchEngine[1], 
                               ByDirectCustomer[1],
                               ByPartnerBlog[1])),
   by=CustomerType]

UPDATE 2: adding ProductID

This is proving trickier to do in a neat cartesian-product sort of way. I cannot think of an elegant way to generate the 31 dates (-15:15) for each purchase (melted matrix would probably be too big). The code below works as intended but is not as fast as the previous 2:

Pr <- data.table(Products)
setnames(Pr, 'ID', 'ProductID')    ## not necessary here, but good practice
CenteredAround <- as.Date(Tr$Date - 30*Tr$Timeliness)

setkey(Tr, ID)
Tr[, ProductID:=sample(Pr[abs(Pr$DateReleased - 
                              CenteredAround[.I]) <= 15, ProductID], 1), by=ID]

Question 2

A very simple optimization is to avoid modifying the data frame in the loop, as others have suggested. At least prior to R3.1, modifying a data frame is really expensive, so that's the last thing you want to be doing in a loop. Also, based on Hadley's comments and release notes for R3.1, it may be the case that modifying data frames is not as expensive with R3.1, but I haven't tested.

Here we get around the data frame modification by storing interim results in vectors, and then only inserting into the data frame after the loop. Consider:

system.time({
  custId <- Transactions$CustomerID
  refBy <- Transactions$ReferredBy
  productID <- Transactions$ProductID

  for (i in 1:100){
    # Only sample customers which share the same 'CustomerType' as the transaction
    custId <- sample(Customers[Customers$CustomerType==Transactions[i,]$CustomerType,]$ID,
                     1,replace=FALSE)

    # Sample the 'ReferredBy' based upon the proportions described in 'Parameters'
    refBy <- sample(ReferredByOptions,1,replace=FALSE,
                    prob=Transactions[i,c("BySearchEngine", "ByDirectCustomer", "ByPartnerBlog")])
    # Only sample products in the required range to maintain the 'timeliness' parameter.
    CenteredAround <- as.Date(Transactions[i,]$Date - Transactions[i,]$Timeliness*30)
    ProductReleaseRange <- as.Date(CenteredAround+c(-15:15))
    productID <- sample(Products[as.character(Products$DateReleased) %in% as.character(ProductReleaseRange),]$ID,1,replace=FALSE)
  }
  Transactions$CustomerID <- custId
  Transactions$ReferredBy <- refBy
  Transactions$ProductID <- productID      
})

Which times in at:

user  system elapsed 
0.66    0.06    0.71

The corresponding time with your original code is:

user  system elapsed 
5.01    1.78    6.79

So close to a 10x improvement with a minor change (avoiding modifying the data frame repeatedly).

I'm sure you can get further improvements, but this is a real low hanging fruit you can easily implement.