IPhone mail settings incoming and outgoing server?

I'm trying to set my email account up on my iPhone. It is asking for incoming and outgoing server details including Host Name, Username and Password. Both Incoming Mail Server and Outgoing Mail Server ask for the same things. I'm with gmail. What do I fill in here?

Texts on iPhone from number that appears to look like +1 (000) 000-0000?

What does this mean? Are they fake messages, or what? Please help, very important, top answer given.

Added (1). No, this is a number that apparently my husband had to meet with last night over a deal and he sent me a screen shot image… But cut most the number out but you can tell its from a weird number…

I feel like my iphone was hacked?

I was hanging out with some people and out of no where they started making comments about things that were in my search history. They were very specific about certain things that I've recently looked up. When I finally noticed what they were saying. I turned my Wi-Fi off on the phone and one of them said 'there's a dog'.It was so strange. I kinda want to kill these people for invading my privacy. Is it possible for them to do that? Is there a way to prevent it? Is there a way to see what they were looking at? Is there a way to completely delete any history, cookies, data, and other information I don't want people to see without removing all my other information like apps etc?

Can I get my iPhone replaced still?

My iPhone got some water in it and now the speakers aren't working. It is still under warranty, do you think I could get a new one from apple by just saying that it happen by itself?