Shopping

Shopping for what??

Shop for clothing, bag...etc... I mean does the mall there close early?

They don't have shopping malls in Rome, Florence or Venice, at least not in the centre, and definately not in Venice. It is all individual shops.
If you are thinking of a modern city like Singapore with indoor shopping malls, Rome, Florence and Venice are nothing like that. The first time you walk out into the streets of these cities (Venice especially) you are going to be hit in the face with a very big piece of culture shock.

Most shops in Italy are closed on Sundays except those which are the lifelines for tourists.

You can get counterfeit bags on any street corner or piazza. The sellers will always be there. Don't do that. The articles are not genuine and you can and will be fined by the fiscal police. The fine starts at €1,000.00.

You don't give any clue of what quality or price point you are interested in. Until you get to the artisinal makers, much of what you see in many shops oriented to tourists is cheaply made in China even if it appears to have Italian markings on it.

Many of the shops in Venice are now Chinese owned.

You will need to look carefully in each city for the shops you are looking for. There are not collections of shops.

How about factory outlet? In Rome, Florence ? Where are they located?

There is an outlet on the outskirts of Rome, but I don't know how good it is:

http://www.mcarthurglen.com/it/castel-romano-designer-outlet/en/