New Year's in Prague! Click Me!

Celebrating New Year's in crazy Prague! :))) Visiting from the 26th of Dec till the 3rd of Jan and I will have a few friends of mine (mixed group), and I was wondering ..

1) Stay connected.
Is Wi-Fi available in most places?

2) Having fun.
Where to party, music, drinks and indeed beautiful fun people :))

3) Shopping.
What will be the best option to do shopping, if you will have only one day?

4) Accommodations.
Cheap recommendations of accommodations? Heard you can rent apartments and it's cheaper, or nice hostels?

Thanks for your help in advance :)))