Do we say "what would it look like?" or "what would it looks like?"

"What would it look like?"
OR
"What would it looks like?"

We use "look" instead of "looks" because of the auxiliary verb "would" in front of the main verb "look".

For example, when we answer the question, we say "It would look like..." instead of "It would looks like...".

Do we say "show interest" or "show interests"?

For example:

"Seven schools have shown interest"

OR

"seven schools have shown interests"?

We use "interest" because "interest" is an uncountable noun.

Do we say "three's a company" or "three's company"?

I would say that "three's a company" is more appropriate as an idiomatic expression. It is a short form of saying "three is a company". 

According to this website, the original idiom is "two's company, three's a crowd".

Then again' "three's company" may be correct too, since in the original idiom, it says "two's company", meaning "two is company".

So, "three's company" can be read as "three is company".

I think both are correct. However, to be closer to the original idiom, maybe we can stick to "three's company".

What's the difference between "assume" and "presume"?

My dictionaries say both words have similar meanings as they are synonyms.

I googled about it and learnt there is a slight difference between the two:

When we assume, we may not need any evidence to prove it is true. 

When we presume, we are saying it is probably true based on past happenings.

References:

http://grammarist.com/usage/assume-presume

http://www.vocabulary.com/articles/chooseyourwords/assume-presume/

http://www.grammarly.com/answers/questions/1073-what-is-the-difference-between-assume-and-presume/