I'm using bitcoin-qt.
So, addresses should not change,
Correct. You can generate additional addresses, and if you lose your wallet.dat file without a good backup you will lose all your bitcoins forever. As long as you keep a good recent copy of your wallet.dat file, you should continue to have access to the coins that are sent to any address that wallet has ever generated.
and address are the sole means to keep a track of bitcoin accountancy.
That's a good way to think about it, but in reality signatures generated with private keys are the sole means to reassign control of bitcoin value to someone else.
So before acquiring an address, does the Bitcoin wallet confirm with the network that there are no duplicated addresses?
No.
Or is it that the client completely relies on randomness and probability to generate a unique address each time?
Correct.
Cause the process of acquiring new address is very frequent in the Bitcoin network.
Yes.
For each transaction, it's recommended to make a new address;
Yes.
considering the no. of transactions, don't you think the possible public/private key pair will exhaust soon, or overtime, the probability of a collision will increase dramatically?
No. 2
160 is a very very very very big number. Humans seem to have a very difficult time understanding just how big such a number is.