Yes; this limit is 100 items by default, but can be changed using the context menu for the log itself.
The contents are not saved, no. You can manually copy them by selecting items and copying them either using the context menu or Ctrl-C.
There is no built-in method for retrieving the contents of the log.
Certain information that is shown in the log may also be available through tokens, however; have a look at the "Text (and Text-To-Speech) Tokens" section of the documentation (Press F1 while VoiceAttack has focus to open VoiceAttackHelp.pdf in your default PDF viewer).