I am looking for an IDE/tool that runs on Android and that would include all the features to build an Android application without relying on external machine.
It could be simply a Java and text editor (it is good if there is no integrated UI design tool), but absolutely bound to a tool to build and package an apk. The idea would be to create an Android application from scratch on a device running Android OS (and not another Linux, or Windows/Mac).
I suggest you take a look at Terminal IDE:
Terminal IDE is an expandable terminal application, with a full Java / C / C++ / HTML / Android development kit, that runs on your Android device.
I've installed that on one of my tablets. With ~50 MB download size (~130 MB installed), it's not the smalles one, but it comes with almost everything you might need for development (hard to tell from my side, as I'm not developing Android apps): gcc, javac, even proguard. It features a terminal, and also includes an SSH daemon to let you remotely connect to your device. On the terminal, Midnight Commander is available as file manager (the probably best command-line file manager on *nix). A custom soft-keyboard (which you can enable optionally) should support you with developer-specific work.
Terminal IDE (source: Spartacus Rex; click image for larger variant)
I'm just using it for terminal and command line access (specifically for remotely managing files), so I cannot talk about its efficiency in terms of development. But it's the only complete dev toolkit of this kind known to me (and I'm pretty informed concerning available apps on different topics, see my profile). Other users praise it e.g. as a powerful tool for developers and programmers alike, so it should definitely be worth a look.
