Hi,
From a local server as Wampserver and from a server "online", you can not connect to a MySQL server other than the server on which you are.
No web host can connect to the MySQL server from a server other than his own.
A web host that would allow such a thing is to avoid like the plague.
You MUST export your Wordpress database to a SQL file from the "online" server and import it into Wampserver.
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Documentation Apache -
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Documentation MySQL -
Wampserver install files & addons