So your're talking about OVER THE AIR as in metal antenna? Again what's the point, that's absolutely useless, but to answer your question, no. Trust me that is not a factor to anyone. You have much better choices to record OTA at a one time payment, it's a DVR. Local channels? Yes of course the genie can. As for #2 Directv has an app. So #2 is a YES as clearly explained below. I understand you have dish and are very happy with it.
Right from their web site:
With DIRECTV mobile apps, the ultimate entertainment experience is always just a tap away. Now watch your favorite movies and shows anytime, anywhere, on your tablet or cell phone with DIRECTV Everywhere. Even watch live TV on your tablet or cellphone anywhere in your home. The DIRECTV app, now also available for Kindle Fire, lets you set your DVR from anywhere. And with your subscription to NFL SUNDAY TICKET MAX and the NFL SUNDAY TICKET app for your tablet or cell phone, you can catch every Sunday game live wherever you are.
Watch select channels LIVE on your tablet anywhere, inside or outside your home
Stream AXS TV, beIN Sports, Shorts HD, Sony Movie Channel, and DIRECTV's exclusive AUDIENCE Networkâ„¢, live on your tablet anywhere you have an Internet connection, at home or on the go.
Resume watching
If you're interrupted while watching a movie or show, the Resume feature lets you resume where you left off when you return to your video.
Set your DVR from anywhere
You can use the DIRECTVâ„¢ Tablet App to schedule recordings on your DVR from anywhere, not just in your home.
Access your DVR playlist
You’re just one tap away from all the recordings you have on your DVR playlist.
Get detailed show info
See descriptions, upcoming showings, cast & crew, parental info, similar shows, and photos.
Get tips and answers
You can get handy tips on how to get the most from the tablet app, as well as quick answers to your questions.
Just tap the question mark on the top-right.
Choose your HD DVR
You can use the tablet app with any HD DVR in your home that’s connected to the Internet.
Customize your settings.
Tap the gear icon on the top right to change your settings for the app so that it works just the way you want it to.
Browse kids & family channels
Looking for a show for the entire family? You can find all the family-friendly channels together in a single module on your home screen.
Set Parental Controls
You control what you see on your tablet. Just tap the gear icon on the top-right of the screen to access Parental Controls.
You can block channels from live streaming, as well as set rating limits for movies and TV shows and hide adult content.