It is reasonable to request reprints of articles. It is reasonable to comment on how much you enjoyed or gained from reading something this person has written, although don't overdo it. It is also reasonable to ask an intelligent question arising from something this person has said or written. This is especially good if you know what you are talking about. It is not wise to make a point of telling someone just exactly what you think is wrong with their theory, their method, etc., on the grounds that they will then be convinced of your superior intelligence.
Most academics are pleased to have others interested in their work.
If you want to explore the possibility of working with them, say so. If you know you are very serious and your qualifications are reasonable, you might ask if it is possible to visit. Not all academics will grant such visits because they can be time consuming, but it will not offend to inquire. If they wish to interview you, you will be invited. In this case, if you are not invited, you will not be welcome to visit.