You do not need apps to keep track of calls and GPS position.
For most carriers, all calls are shown in the statement and most update this every few days or more often in the online view. For any line you can see what number was called and for how long. Since this information is coming from the carrier, you do not need to worry about anything being deleted by the child. If you pay the bill, you get to see this information for all lines on your plan. In most cases this will also show you who SMS/MMS were sent to, but not the content, and not email information since that is not a carrier service.
As for GPS tracking, you do not need an app for that. This is something which can also be done through the carrier or through third party GPS monitoring solutions for a fee. In most cases, this requires an opt-in, but since you can take your child's phone from them and opt-in, you will be able to do this. For example, on Verzion there is Family Tracker, which even lets you setup geo-fenced alerts. There are also third party services which provide opt-in tracking.
It is not usually illegal to install software to track and monitor your own property, and in many cases it is okay for a parent to track their child in such a way. For legal concerns though, please ask a lawyer as I am not a lawyer and therefore cannot provide legal advice.
With any type of app or local tracking, a smart kid will always be able to figure out how to disable the tracking or to send false data so any app has a likelihood of being circumvented. There are also alternatives like Google Voice, email, etc. or some encryption services that those who want to make it difficult will use. Likely, the best response would be for the parent to develop a trusting relationship with their child and to keep up with what they are doing and where they are going.
Something you may want to research more would be working on a rooted phone. It may be possible to password protect access to the rooted controls and you may be able to put something there and have it be hidden from the user mode apps since you are doing this as root. You would of course have to root the phone. A quick search shows at least one example of a GPS app that can installed as a service with root in the background. I am sure someone makes such things for call recording, logs, etc as well which might be worth further research.
Since you wanted more information on India, it looks like perhaps you could ask the government, as there are plans to track all mobiles in real time. At least for a kidnapping or runaway I would imagine the police could leverage this, later to dinner, probably not.