음..What is the difference between "해요" and "하여요" in korean present tense?

Hmm, I think maybe you're thinking too difficult here.

해요 really just means, -do. that is most commonly used I think.

숙제해요. 공부해요. 요리해요. etc. 

on the other hand, 하여요, sounds a bit unnatural to just use like  해요.

숙제하여요, 공부하여요, 요리하여요 - would sound a bit off and in fact, people wouldn't use it like that. 

Can you give other examples of 하여요 that you know of? Maybe I can help you from there. 

But from what I can say now is that, we don't generally use '하여요'.  

I'd never heard 하여요 until today, lol. I was looking up the past tense and a lesson from Talk to me in Korean came up and the pdf for that lesson was listing the endings for the verbs in present tense and it said: 아요, 어요, and for verbs with 하 stem, it said to use "여요". I found it really weird and in my text book it was never mentioned.

Here is what the pdf said:

Verb stems ending with vowels ㅗ [o] or ㅏ [a] are followed by 아요 [a-yo].

Verb stems ending with vowels OTHER THAN ㅗ or ㅏ are followed by 어요 [eo-yo].

Verb stem 하 is followed by 여요 [yeo-yo].

So maybe I should just use 했어요 for past tense with verbs with 하 stem?