I heard that I can damage my sensor by cleaning it.

Yes you can, but generally not if you do it right. 

First, you aren't really cleaning your sensor, you're cleaning a filter that sits on top of it. Can you damage that filter? Sure, just as you can damage any optical surface with bad cleaning technique. Is it likely that you'll damage it if you use established techniques with well-known products? No. See my cleaning article for more.

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