With 9volt on the DC socket you can't draw more than a few hundred mA from the 5volt pin for sensors. And 5volt on the DC socket is too low. The DC socket needs 7volt minimum.
Better to use a 5volt cellphone charger where you can plug the Arduino USB lead into.
1Amp is more than enough, because of a 500mA fuse inline with USB power.
What are you planning to add to the Arduino.
Leo..
I assume you mean LED strip.
Then it's better to use a 5volt supply with enough current capability to drive all LEDs.
And power the Arduino from that as well, on the 5volt pin.
So tell us which type of LED strip (weblink) and how long (how many LEDs).
No, you most likely can't.
You can't power a LED strip through the Arduino (assuming you mean that).
Leo..