Heya! Congrats on making the portal. Good stuff you got there.
Here's some suggestions for the intro texts:
Part 1 - Current
"Do you want to know how do you use your smartphone?
You have installed this app, so the answer will surely be affirmative.
With this app you can know with what apps you lose your time; time which you could lose living your real life..."
Part 1 - Suggested
"Would you like to know how you use your smartphone?
Well, as you've already installed this app, that'll be an affirmative!
By gathering statistics about your apps with Phone Usage Monitor, you'll know where your precious time is creeping off to. Time you might want to spend on living your real life..."
Part 1 - Motivation
The second "do" doesn't really have a function in the first sentence and I made it a bit softer to make a more friendly first impression. I mentioned the app's name to remind the user what's going to help them (branding, be proud of your creation). I stayed true to your intention, the reference to 'real life', but made that a bit softer as well by using "might" and not mentioning a negative word like "lose". We're all winners here!
Part 2 - Current
"To let us know this information we will run a service in the background to monitor the use you make of your smartphone.
Quiet!, it will not consume more than a little bit of the precious battery of your mobile..."
Part 2 - Suggested
"You're probably wondering how much battery this app will consume. Don't worry, just a tiny bit.
Think about the time you will save after gaining all this usage intel. You won't even need as much battery anymore."
Part 2 - Motivation
Shouting "Quiet!" doesn't come across very friendly. There's also never a comma after an exclamation mark. I wrote the text to match the battery icon better. I'm also pushing the major goal of the app forward.
Part 3 - Current
"We will give you more information if you let us see how do you use the apps in your device..."
Part 3 - Suggested
"Sorry to bother you but I will need some usage access in order to provide you with all these awesome statistics. Is that okay with you?"
Part 3 - Motivation
"let us see" gives the impression multiple people or a company will be watching along, which totally isn't the case. I wrote it a bit more personal, fun and friendly.
Part 4 - Current
"Do not worry!
The data we collect is NOT sent anywhere."
Part 4 - Suggested
"Do not worry!
The data I collect is NOT sent anywhere."
Part 4 - Motivation
As in part 3, It's better to speak from a first person point of view, "I" instead of "we". It's just the app and the user, "you and me", which is a more comforting thought.
Instead of "START APP" I'd use something more vivid like "Lets go!" or "Show me some numbers!" or "Start saving time!"
The UDPA looks good, people are used to not reading these disclaimers and accepting them anyway. It's also a nice reminder that even if there is a "we", it's literally stating no personal data will be collected on any server. Kudos!
I personally don't like the last paragraph but ah well, one has to make a living, right?
Looking forward to those stats...