Mendix can, at the very least, do bullets two through 5. I won't comment on the first bullet – it may be that there is a library that covers this, but I am not familiar with it.
Note however, that Mendix is not a BPM tool, and comparing it with BPM tools may lead to weird conclusions. Mendix is a platform to visually create applications. It is an abstraction of Java. As such, what you are actually asking is: “Does Java support the following features”. The answer is: “Yes, but you will have to create all of this yourself, excluding functionality covered by libraries.” The same is true for Mendix: Mendix can support your bullets two through five, but you will need to create this functionality yourself. This is very different from buying a BPM tool that already has these functionalities included.
Thank you!