Recent Posts+, how to solve multiwidget?

Easy, Anton!
You don’t have to hack the database…

Probably you can find a replacement for this plugin that uses the modern Widgets_API, responsible for the multi-instance widgets. At least as far as I know, because haven’t worked much with WordPress pre-2.8.

If you are willing to hack something, hack the plugin using the examples of the Codex.

As for showing one widget in the Front Page and other in the rest, use the plugin Widget Logic. It is very simple and effective.