I have a temporary residence permit for Croatia. Can I travel to other EU countries, such as Germany?
The Croatian permit does not exempt you from the requirement to have a visa to enter the Schengen area. So, assuming you're not traveling with an Annex II passport, and you have no other basis for a visa exemption, you can only travel to Germany if you get a Schengen visa.
What other advantages do I have with this card?
I am not aware of any. If Croatia joins the Schengen area while the card is still valid, however, it will allow you to visit other Schengen countries, subject to the 90/180 rule. According to Wikipedia, this might happen next year.
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