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Do I need any key or registration to show OSM maps in my blog

No, OSM is under cc-license, you do not need any API-key!

Can I use several maps in the same poost/page

Just use as many shortcodes as you want to, even within one post.

There are already geo data in customfields in my blog, can I reuse them?

Yes, the format has to be Lat,Long. The name of the customfield has to be configured.

I tagged my posts/pages with another plugin, can I use this tag wit OSM plugin ?

Yes, up to now WPGMG (google-maps-geocoder) plugin is supported, others will follow on request.

Why is there no map in the "Edit post" page ?

Since most people do not add a map in every post I decided to put it in the settings page. If there are some requests to put it in the Edit post I will make it configureable.

How can I use this plugin for my geocache posts ?

You have to install gcstats plugin to use geocaching feature of OSM-plugin.