Coming from an iPhone, this was one of the things that bugged me, no waking of the screen when receiving a text message. After doing research for a few days, came across the app called SmsAwake. SmsAwake allows you to set how long you want the screen to be on after you receive the text. Hope this helps! Enjoy.
Still haven't discovered anything for those. Just for SMS waking. You maybe able to get your phone to wake for mail and etc. if you root your phone. But without rooting and custom kernals, prob can't but done, at least not that i know of.
I use Sliding Messages.
The app wakes up your phone displays your message, allows you to send a quick message back and unlocks it if it's locked.
The problem with me is that somehow this app disables my Voicemail notifications and the MMS is hit and miss but for that I use the stock messenger.
There's a free and paid app.
Good luck!
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