My job now has Wifi.. can they find out if i use it if i enable wifi on my phone?

Nope, since there's no authentication there's really no way to tie a specific device to a specific user unless they actually saw you using it and put two and two together. It may show your device's hostname, so if it's something obvious like JOE'S IPHONE then I would probably change that. I highly doubt they even check it though, it sounds like you don't have any kind of full time IT staff whatsoever.

Couple of things here. 1: Since you work in the office, I don't see why you can't let your phone use the wifi network . I let my phone connect to the Wifi network in my office, as does everyone else. 2: The admin might see some device he doesn't recognize attaching to the network. He probably won't know who it belongs to, nor will he care. If he DID care, then he would have turned on WEP. 3. If you're really that concerned, casually ask the admin about it. Most likely he'll offer to show you how to set up your phone to connect to the network. 4. Finally, use common sense. Letting your phone sit on the Wifi downloading updates and emails or whatnot is fine. Using your phone to surf the internet during lunch or your breaks is fine. Using your phone to download porn, or stream movies....probably not such a great idea.

they can see that you are connected to it. at least i have a similar router and when i go into the settings it shows all connected devices. if you want to browse whatever and not have them know just in case they are monitoring the connection this can be done as long as you have an android phone. you can root your phone and then download the ssh tunnel app it routes all your connections through an ssh tunnel. i thought i'd just throw that in in case you decided you wanted to do more non work related stuff down the road but if you are only checking the news quick on break i don't think they will mind.

They can tell something is accessing it yes. If your phone has a name I.e. Johns Cell that would show up as a connected device. If it doesn't have a name it probably is a weird set of characters and numbers and that is what would show up on their accessing list

Why not simply ask for the policy on using the WiFi? That way you'll know for sure instead of relying on opinions here. Being open, I wonder if it may be intended for use by visitors. And yes, a specific device connection may be tracked. The router records the MAC address of the WiFi chip inside the phone. As someone pointed out though, they would have to prove it is your phone. But if a device shows up every day during the same time period of shift, it will certainly point to an employee. If you intend to just using the WiFi without clarifying the policy, I assume there is a usage policy for your computer at work, so make sure you follow the same rules on your phone.

Yes, but they'd have no way of knowing who's phone it is or anything like that, and there isn't much chance of them finding out anyway :)