***** NOT A TEACHER *****
1. I was wondering whether it would be helpful to remind you that in English you can often change an adjective into a noun
by simply adding the word "the."
a. I have found that the rich are more courteous to me than are the poor.
2. I am going to study hard, and I want you to do the same.
a. My dictionary classifies it as a "pronoun."
3. "He looks the same as you."
a. Here is a somewhat similar sentence from a grammar book.*
i." Your schedule is not the same as mine."
(a) "same" is a noun. (Don't worry: some books call it a pronoun; others call it a noun.) "The same" is a subjective complement. That is, it refers to "Your schedule." The whole sentence is "Your schedule is not the same as mine [is]." It is not necessary to say "is."
(b) Based on that example, I believe that we can analyze your sentence this way:
(i) He = subject.
looks = linking verb. This is NOT an action verb in your sentence.
the same = the subjunctive complement.
as = conjunction.
you = subject.
look. = verb that is usually not expressed.
4. In my opinion, "He looks similarly as you" is definitely NOT the same as "He looks the same as you."
a. "similarly" is an adverb. = [do something] in a similar manner.
b. "looks" in your sentence is an ACTION verb. [For example, "He looks at the beautiful girls."]
c. I do not think that sentence is well-formed. That is, it is very difficult to explain its meaning. I think that it seems to say something like:
You look at the beautiful girls in a certain way, and he looks at them in the same way as you [look at the ....].
As you can see, that is definitely NOT the same as "He looks the same as you."
* R.W. Pence and D.W. Emery wrote A Grammar of Present-Day English (1963), page 226.