Is it recommended to email a professor at other institution to work with him over the summer
Sure, just reach out with SHORT emails.  I would not expect too much reply since it is a cold call but "a shot on net is always a good play".  Mention a sentence or two to indicate you looked at their webpage or pubs and have an interest in their work.

In addition, try to send some inquiries (similar format) where have some connection (e.g. you mentioned friends had visited specific places in Italy, England).  Professors like to get some "pipeline".  (E.g. "we have had periodic Elbonia Uni students".) Just gives some slight familiarity for you/them and some feeling for them that they may get more positive experiences in future.  However, note that expectations for undergrad visitors is not high.