Can't speak for OpenElec but Raspbmc supports Airplay and will show video thrown up to the big screen from my iPhone.it doesn't like video from the iPad but audio is fine.
I've not tried that, I use the official XBMCRemote app, it's free and available for iOS and Android.Download the Yatse app to my phone so I can control the whole thing from that if I want to.
I also changed my Services > Webserver > Web interface to AWX, it seems to offer more than the default one. The IP address of your Pi will get you there.
1Channel and Icefilms for streaming movies from the Internet. ArtistSlideshow for when you're playing music, it downloads artist images and makes a background slideshow while the song plays. Might need some xml tweaking, I can upload my working file if needs be.you'll need to add some of the unofficial stuff and there is a lot out there.
Appearance > Skin > Settings is easily overlooked but can give you useful shortcuts to add-ons on the home screen.