Try the following troubleshooting steps in order, testing between each step. 1. Power the phone off and back on again 2. Reset all settings by going to Settings - General - Reset (this will change your wallpaper and ringtones back to default, along with all other user changeable settings but will not delete any data) 3. Make a backup of your data on itunes or icloud then restore to factory settings by using Erase all content and settings under Settings - General - Reset NOTE - this will erase all content on the phone be sure to have a secure backup.
The success of the SMC reset tells us that the top case is working, including the power button and that the machine is getting power. You can try a PRAM reset by pressing the power button and holding Command + Option + P + R and listening for a chime, this is worth a try but truthfully is not likely your answer. If you open the machine up you can try disconnecting the battery and leaving it unplugged while trying to boot off power directly. Past that the most likely scenario is some sort of issue with the main logic board.
If no image appears on the external monitor you're likely left with a video card issue. Your laptop has integrated video so it is not a replaceable card, you'd be looking at replacing the board. Considering that there are no images at any time it is likely that your data is still intact and can be recovered by removing the hard drive and placing it in an enclosure or a dock and connecting to another computer.
With liquid damage its difficult because you'll need to determine which components are compromised. Follow the take apart guide and you can look at the components. The 11" Air has fewer boards in it than some of the other Macbooks so it should be easy but can potentially be costly. You're looking for any sign of liquid - dried up wine, corrosion (a blue green buildup), there are also small white dots that will change to red if they come into direct contact with liquid. Personally I would replace corroded components, some people swear by being able to clean them but I wouldn't trust it. If it works for now take this opportunity to make sure you save your information to an external hard drive.
Yes that guide will work for you, just be careful disconnecting the LVDS connector and with the straps that hold in the airport antenna cables, they can tear very easily. When reassembling make sure the antenna cables are flush inside and just under the logic board, if they aren't you will have trouble getting the display to fit in properly.
That is a ground for the antenna. It should come attached to the top case but can be removed by taking out the small screw that is at the top of it, but it also may be attached with adhesive. (I am a former apple tech and never actually removed it due to it always shipping attached to the new top case.)