I don't know for you but I always felt like Android especially is not safe. Is somebody - the government or other - able to listen to my microphone, or access my hard drive remotely?
Why do you think Android might be especially vulnerable? I expect the NSA has the tools to snoop in on practically anything connected to the Internet.
I'm wondering if secured apps like Textsecure and Redphone really help or are just an illusion. Indeed it is pointless to secure the transport if the source and the destination are corrupted with a security hole at the hardware level.
Indeed, but it sounds pretty expensive to built a security hole at the hardware level when a software one will work admirably.
Can the monitoring of our network really tell us if we are spied ? The data sent to government agencies could be excluded by the author of the network monitoring app.
Most likely, such data would not reach the network monitoring app at all. After all, all a network monitoring app does is use a public API to sniff the data; it doesn't have a direct link to the fabric of the universe, right? The way to check would be with a passive cell signal receiver ... and you'd have to transfer the encryption keys used by the phone to it in real time; massively complicated stuff. But it'd be relatively easy to spot "extraneous" packets included in that capture but excluded by a network monitoring app.
Also, at the software level, can we really assume that Android is safer since it is - supposed to be - open-source ?
Not unless you obtain a copy of the source, the whole source, and nothing but the source, and compile and flash it from a toolchain known not be compromised. And even then only if you trust that vulnerabilities in "open-source" software are rapidly found. Historically, this hasn't been the case. Consider how long the heartbleed vulnerability was around before it was found, and the underlying bug wasn't even hard to spot.
Well lot of questions, but I'm trying to find a middle ground between concern and paranoia.
The simple thing to do here is just don't do anything that might raise flags for the NSA. They really don't care about your communication with your girlfriend(s).