早上好 The words are nearly identical in each group, so there is no rule to use them..

group 1 is looking for in indefinite amount of time. stare is to actively look with intensity at something, can be aggressive gaze is more passive, i.e. looking at something but not necessarily actively looking, peer is normally used with an object peer around/over/under and object. group 2 are all looking for a short period of time. glance see something briefly while moving, glimpse see only part of something, catch a glimpse of something i.e. not see all of it or only really briefly not long enough to really see it. skim this is only used with reading... I think skim a book, not read it in full, read it lightly quickly to get an idea of what is in it but not know all the content. Stare is very intense active looking almost aggressive where as gaze is looking passively. I stared at the item intently and couldn't figure out what the problem was. I gazed passively over the lake at the sunrise, wondering what surprises the day would bring.

the difference between two groups is how long your eyes are fixed on a subject. group one has verbs where your eyes are fixed on a subject for a long time. group two has verbs where you eyes are fixed on a subject for a really short time. Stare is used when you are looking at something without some form of control. For example. if a guy stared at you, you would think he is a creep! Gaze is usually in a romantic sense (not just in the love sense but also something that stirs your emotions) for example: I gazed into her beautiful eyes!!! or I gazed at the star filled sky. hope I helped.