Questions about remote control spyware, remote enable network settings?

I have a few more questions :) Can you android phone be remotely accessed/controled without a trace for the user? I am not talking about just slipping information, i mean literally if someone had installed something on my device can he like wake up my phone in the middle of the night, unlock it remotely and start messing with it? I know that some programs can allow remote access but can they boot the phone from sleeping, unlocking and so on? Also, if you turn off your wifi and mobile network, can they enable it and then access it? Will it leave trace (like if he is using program that intercepts sms, does the sms acctually arrive in your message box) If such program is installed, can it remain completely hidden? Does factory reset get rid of it? If your phone is currently not rooted can such spyware keep working (if we assume the evil person rooted it and than unrooted it) And finally if alll this is possible, can one remotely control your android (like sending a message from your android device, accessing facebook via your own phone and so on) wihtout you seeing the control itself, like your phone is locked and asleep but someone is still accessing it?
Sounds paranoid but i need answers. Thanks :)

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