This is the station 'Blanche' on line 2 of the Paris Metro. If it is more convenient for you to take line 13, you can get off at La Place de Clichy which is less than 300 metres from the Moulin Rouge, about 4 minutes on foot.
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To reach the Eiffel Tower by metro you can buy from 1.90 € a single ticket. However, if you have the Paris Pass on your vacation you can use the public transport network of the city (bus, RER, metro or streetcar Montmartre tram) for free within zones 1-3. The Eiffel Tower is located in Zone 1.
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Yes, tap water in Paris is perfectly safe to drink and is readily available wherever you go, even at public water fountains. As long as taps aren't labeled eau non potable—meaning “not for drinking” in French—everything else is potable. In fact, drinking water from the fountains of Paris has been encouraged.
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