For our eLearning project in our university, we are using Java applets to show some interactive stuff (like some interactive function plotting or some simple question/answer
Most of these problems would appear from the description to be problems with the way the code is written. Unfortunately in our industry, quality is rare.
If an applet takes a minute to load that could be a DNS problem, or some other I/O related issue. (Is it dependent upon network, file or CPU?)
On modern computers memory usage is surprisingly difficult to measure effectively. The overhead of the JRE on a modern computer with gigabytes of memory should be pretty small.
If you use Swing, then the PL&F can be set to be cross platform (Metal, Nimbus or a downloaded implementation).
Fonts can also be dynamically downloaded.