For the OP's question:
1. For iOS you can use Find My Friends to track via GPS, or alternatively, Find my iPhone. You can't track browser history or photos remotely that I know of.
2. For Android you can use apps like "SMS Tracker Agent" and others to do what you described. Search on Google's store.
As far as all the comments, I think different parents have different parenting styles. I gave my teenage daughter an iPhone 3G - I saw a good deal on one at work ($70 for the phone plus accessories and it came with a seriously tough pink Otterbox case included), and so I bought it, unlocked it and stuck it on T-Mobile's $15/month unlimited texting w/ 100 min calls (no data). Yes, it's an iPhone, but most dumb phones are around $40+ used... so it's not like the iPhone cost me that much more. She doesn't have data though and I locked down usage of most of the apps and she and I agreed to a verbal contract when I gave it to her regarding it ("keep it charged, keep it with you, don't use it in classes, don't use all the minutes, don't use it late at night when you are supposed to be sleeping", etc.) I disabled a lot of stuff on it - it has no data access anyway and no MMS access either - so a lot of the OP's concerns don't matter in my case... she can't do YouTube, browse, MMS text or anything else really. She can text us and her friends and make (a few) calls and listen to music, take photos and play games... and that's pretty much it.
And then for people that I'm overly censoring her... well, she's my daughter. I do what I can to try to be a decent father as best that I can. And she personally hasn't complained about any of it and instead seems very pleased that she has an iPhone at all.
I will say that with all of the stuff at school that she does, it's handy to be able to communicate with her so that if she stays late for some reason and we need to drive over to pick her up, we can talk to her. It's been pretty useful.
Lastly, for what it's worth, I'm not a hypocrite... my wife and kids can track me any time that they want using Find My Friends or Find My iPhone. I actually encourage them to when I'm cycling since I often ride alone which can be a bit unsafe. And they can borrow my phone whenever they want for whatever reason and if they want to look at my messages or browser history or whatever... it's fine by me. I hand the phone over to my family all the time to look things up since I have the fastest phone/data connection.