What if the system crashes if I have made transactions after my backup? Suppose I have a recent backup of my wallet.dat file.

Now I make (say) two transactions: one receipt and one send.

Before I run my next backup, the hard drive crashes and I lose wallet.dat.

I can restore wallet.dat, of course, but only prior to the new two transactions.

What will happen to those two transactions?
Assuming you had a chance to send those transaction out, they will still be processed. So long as the transactions didn't create any new change addresses, your wallet will still have all the information needed to spend any Bitcoins you have left.