1. Can a man remove hair any hair on his body that he wants?
2. If eyebrow hair bothers a man can he remove it?
The Torah prohibits a man from beautifying himself in the manner of women, and it is therefore prohibited to shave one’s body in places that it is the way of women (and not men) to do so. The Talmud (Nazir 59b) specifies pubic hair and armpit hair as being prohibited for men to shave. According to Rashba (Vol. 4, no. 90; see also Beis Yosef, Yoreh De’ah 181, and Bach 181:8-9), this prohibition applies to the entire body. However, the Rambam (Idolatry Chap. 12:9) writes that the prohibition (in his opinion, rabbinic) applies specifically to places that it is the custom of women alone to shave. This is also the ruling of the Rema (Yoreh De’ah 182).
Therefore, if it is generally accepted for men to remove hair in a given part of the body, it is permitted to do so. For parts of the body where it is not generally accepted for men to remove hair, it is forbidden to do so for the sake of beautification, but it is permitted to do so if one requires this for purpose of medical treatment, or other non-beautifying purposes (see Darchei Moshe, Yoreh De’ah 182, concerning shaving arm-hair for somebody who is ashamed; see also Tosafos, Shabbos 50; Iggros Moshe, Yoreh De’ah 2:61; Seridei Eish Vol. 2, no. 40 — the final two sources refer to the prohibition of coloring one’s hair, and write that it is permitted for non-beauty purposes).
Note that according to several authorities, the concept of something that is “generally accepted” to do is defined by the ways of Jews, and not by non-Jews alone.
The same principles apply to eyebrows. To my knowledge, it is still the general manner for women to trim eyebrows, and it would therefore be prohibited to trim them for the purpose of beautification, but permitted if they cause embarrassment or physical disturbance.