Hi Rafael,
I'm a native English speaker from the US. I'll try my best but maybe others can add on.
Like:
You can like something, which means you enjoy it. For example, "I like pizza."
Something can also be like something else or similar to it. For example, "A cheeseburger is like a hamburger but with cheese on it!" Like in this way is also sometimes used as a metaphor. For example, "The clouds are like cotton balls."
Look Like:
Something or someone can look like or be similar to something/someone else. For example, "She looks like her mom." (The similarity is based on her visual appearance.) You could also say, "She is like her mom," but if you say this, I'm not assuming the similarity is based on appearance. Maybe she is like her mom because they both speak loudly.
We also use this phrase in a way that implies that maybe we don't know for certain but we think something. For example, "It looks like she is sad." or "It looks like (it will) rain."
Alike
Alike also means similar. For example, "The mother and daughter look alike." Or if you wanted to say, "The mother and daughter dress similar," you could say "the mother and daughter dress alike."
"It's important to him that he treats his two kids alike and doesn't favor one over the other." (He treats them similarly, with no difference)
I don't know if this helped.
~Michele