On the bass clef, there are 2
C notes. I think it is a tie (wiki) and they should be played once for 6 beats. Am I correct? Or do I have to play the C twice, 3 beats each?
It's not always easy to tell, but here we are definitely talking about a tie. How to distinguish? A tie is sole functional and can only connect equal pitches (there is the tricky exception of a tie connecting enharmonically equivalent notes in a modulation but the execution would be to hold the note without noticeable intonation correction).
Does that mean that any bow connecting two identical notes is a tie? By no means. If the first note has any duration modifying sign (staccato, staccatissimo, tenuto, portato), this cannot be a tie. If the second note has any accent mark, it's not an isolated note. Duration modifiers are suspicious but not complete evidence: least suspicious is likely a staccato that may halve the duration value of second note part.
So what happens when we don't have a tie? We have a slur. Where it isn't solely an execution mark (string instruments are instructed not to change bowing direction, and for strings one would not really write a non-tieing slur without a tenuto mark or similar), it indicates connected execution. Connecting two notes of same pitch closely is almost the same as a tie but not completely: is this a melodic phrase with two notes? Like, are there similar slurs used as phrasing in the vicinity that connect unequal notes?
Now if we take a look at your excerpt, we have whole-measure notes connected across the bar line: that's not really melodic (though it could be if the two measures before were also connected but of different pitch). But the complete clincher in your case is that there is another outer bowline across the notes that clearly indicates legato phrasing.
So the phrasing question already has an authoritive answer. The bow connecting only the two C4 notes consequently has to be about something else. So it's a tie.