They are similar phrases, except for "look after" which only resembles the others :) Peachey gave a good description of the sentence structure differences. I think there are some slight meaning differences as well. X is similar to Y: Means X and Y are close to the same. X and Y are alike: There is some similarity. This feels a little more formal than "similar". X resembles Y: X seems, on the surface, similar to Y, often visually. It might or might not actually be similar. It's a slightly more formal word, although there is one common phrase "family resemblance", which means the way two relatives look similar. X looks like Y: Like "resembles", but less formal.

X is similar to Y. X looks like Y. X resembles Y. X and Y are alike. / X and Y look alike. So you see, the sentence structure changes. I'm not sure why you included "look after", because that means "care for". However, a child can "take after" his or her parents. This can mean physically, or regarding personality.