All those phrases have 그래 in them. It can be confusing because it has multiple subtly different meanings.
It is short for either 그러해 (그러하다), or 그리해(그리하다), which is the same as 그렇게 해 (그렇게 하다).
- 그래요: 1) 그러해요 - It is so; That's right, 2) 그리해요 - (You/We) will do it that way.
- 그래도: 1) 그러해도 or그렇긴 해도 - even then; even so; still. 2) 그리해도 - even if I/we/you do so.
Examples:
1) A: 참 좋으시겠어요! (You must be very happy) B: 그래요 (You're right. I am). = 그러해요 = 맞아요.
2) A: 오늘부터 시작할까요? (Shall we start today) B: 그래요 (Ok, go ahead). = 그리해요 = 그렇게 해요.
1) A: 결과가 나쁜데요. (The result is bad) B: 그래도 최악은 아니에요 (Even so, it's not the worst). 그래도 = 그렇긴 해도.
2) 최선을 다해라. 그래도 안되면 할 수 없다 (Do your best, and if you still fail, it's out of your hand). 그래도 = 그렇게 해도.
- 안 그래도(1A) = 그러지 않아도 = 그런 일이 일어나지 않았더라도 (난 그렇게 하려고 했다)
It describes a coincidental situation, like "Even if it hadn't been for that, I was about to do [something similar] anyway".
So it's a bit like "speaking of the devil", except it's wider in usage than just encountering someone unexpectedly.
Here's a scenario: I'm about to call my friend when the phone rings. I pick it up and find that it's him.
(I say): 어, 안 그래도 (너한테) 전화하려고 했는데: Hey, speak of the devil, as I was just about to call you.
- 안 그래도(1B) = 그러지 않아도 = (이미 어떤 상태가) 되어 있는데 (그에 더해서 새로이 비슷한 일이 또 생기다).
It's an extension of 1A), where there is no coincidental event but a pre-existing state instead.
Ex: 안 그래도 피곤한데 야근까지 해야 한다: I am already tired, but on top of that I have to work the night too.
- 안 그래도(2) = 그러지 않아도 = even if you/someone don't do that.
Ex: 안 그래도 돼 = 그러지 않아도 돼: Even if you don't do that, it's Ok = You don't have to do that.
- 그저 그래요: 그저 means "nothing special", so 그저 그래요 means "It's as usual with nothing notable", or "so-so".
- 그건 그래요 (I think this is what you meant, since there's no phrase like 그런 그래요) = 그것은 그래요.
-그것은(That is) 그래요(so) means "That is so", "That's as you say", "You got that right", etc.