For Java see http://forum.meego.com/showthread.php?t=34 and http://wiki.meego.com/Java "Memory is too full" is vague. The values in "Settings > Device > Data Storage" would be interesting to know first.
MyDocs is vfat, so NO its not possible to install any additional programs and games in MyDocs folder. (Advanced answer is that you can repartition your device give system more space from MyDocs, but for most people that leads to MALF or openmode if your not carefull enough)