Most of the shops are open on Sunday

I would definitely recommend a visit on Sunday, not for the shops but for the spectacle of people wondering on the İstiklal Avenue, the pedestrian street linking Taksim Square to Galata.

It’s open everyday. It’s a public square. It’s whether the restaurants and bars are open around it that is the question. But yes, Taksim square itself is always open.

Not sure, but it’s still in progress. Sorry.

Yes, one of the Standard Hotels which is near Taksim square with reasonable price and service is Golden Age. it is near Taksim Square and it takes around 10 minutes to the square on foot. Also, it is near to the subway station too. The other point is there are lots of cafes and good restaurants around it.

Very safe. Just don't go wondering into any bars down side streets.

Taksim square a beautiful open place to set and enjoy the scenery, at it end you will star Istiqlal street, this street is about 2 km long and it’s full of shops. You will find all kinds of things, some reasonable prices and the brands are good prices. At its end you will see. Galata tower, a must see place, it has shops with a very cool stuff.

Gracias

I think it's better to arrange with the your hotel if you are staying in! just to make sure you got a taxi! or you can arrange it by yourself by coordinating with a taxi by yourself!

Sorry, but I cannot better the three choices that Pritipase have given you in their response. Hope you enjoy Istanbul. Regards Ken