I’ve used JEuclid for rendering MathML in my Symja project (Java symbolic math system – point 4 of your list).
JEuclid may be too slow (especially at startup) to render MathML on a mobile phone.
Other alternatives for rendering math expressions with TeX:
and for re-arranging equations or as general Java math libraries:
- Mathrider (Yacas for Java)
- Jasymca – Symbolic Calculator for Mobile Devices
- Java Algebra System
- Hipparchus – library of lightweight, self-contained mathematics and statistics components
- The Apache Commons Mathematics Library
Calculator projects for Android:
- Calculator N+ (GNU public license)
- Jasymca for Android (GNU public license)
- Arity calculator for android (Apache license)