It is haram for a man to have a girlfriend and it is haram for a woman to have a boyfriend. The evil consequences and misery caused by such relationships are obvious to anyone who observes real life. For more, see the detailed answer.

It is not permitted at all for a man to shake hands with a non-Mahram woman.

Deliberately looking at a non-Mahram woman and continuing to look after a first accidental glance is prohibited. It is forbidden to look at any part of her body, whether you think she is beautiful or not, whether it provokes sexual desire or not, whether it is accompanied by evil thoughts or not, and whether it leads to immoral deeds or not.