Is it rude to ask via email to a professor if there are any internship opportunities?
I don't think this practice is rude, but if these are not people with whom you have any connection, and who have not advertised a position, then I don't think you should be especially surprised that you aren't getting many responses.  In all likelihood, the answer is "no" and they don't feel like anything will be achieved by telling you that.  

A few things which might be hurting you:


The email above really reads like a mass form email.  You aren't making any argument about how your expertise is relevant to their specific work, and you're putting the burden on them to think about how your skills might fit with what they're doing rather than thinking about it yourself.
Maybe this is different in other fields, but it's not clear to me what "internship" is supposed to mean here.  A paid position?  Unpaid?  You may be being deliberately vague, but if you're not responding to an ad for a specific position, you have have some clarity about what you're looking for.
I think that the slightly awkward English doesn't really help.  "Chemist for the conservation of Cultural Heritage" sounds very strange to me.  I think "Chemist specializing in/interested in/working on the conservation of Cultural Heritage" is much better.