"What is the time now?" Is correct but it sounds very formal.

I think native speakers would just say "What's the time" most of the time, but there's nothing wrong with other variations. Since I moved to Canberra, a lot of people have asked me "Do you have the time?". This sounded very awkward to me, but now I use it all the time out of habit. When I say it in Queensland, people sometimes give me strange looks for a few seconds before answering. There's a few ways of asking for the time: How late is it? Do you know the time? Can you please tell me the time.

Actually yes, your friend's right. Both of those sentences mean the same thing. I have the same thing happen to me in my language learning.

Yes, it's perfectly acceptable.

yep, it's perfectly fine to use any of these :D English has alot of ways to say certain things.