Answer "I understand" or "I understood"
 

In Conversation:
A)I understood (what you just said).
B)I understand.
Which one sounds better.

Normally, I often use present simple tense with "understand,know and the fact".

For example:
I kicked something.
A)That is my foot.
B)That was my foot.
Which one sounds better.

Re: Answer "I understand" or "I understood"
 

And For the word "see".

[I stand in front of the blue car.]
A)Do you see his blue car.
B)Did you see his blue car.
Which one sounds better.

Re: Answer "I understand" or "I understood"
 

1. Generally, the present - because it's true that you understand at the time of speaking:
A : I'm sorry, but I won't be able to help because I have to visit my grandfather in hospital.
B : OK, I understand.

Using the past tense here would refer to previous understanding, and might sound irritated : Yes, I understood fifteen minutes ago, the first time you told me. Don't go on about it

2. Either. You might shout more or less simultaneously with the action - Oi! That's my foot! or say it afterwards, seeing it as a past action - That was my foot which you just kicked!

3. I'd probably say Can you see ... rather than Do you see... but it's still the present. In any case, if the car is still there, the past is logically impossible. Even if you were standing in front of it, it would still be visible :) With a completely obscured object you would use the past though - eg in a memory test : I lay out five playing cards on the table and then turn them face down and ask Did you see the three of hearts? Here the action of seeing the card is past, because I've obscured them. So the past verb is logical.

Re: Answer "I understand" or "I understood"
 

My answer is "Yes, I can see that" or "Yes, I see that".
I don't have to use "I am seeing", do I?

I'm confuced..because I think that present simple tenst is used for habits,feeling, or permanent facts only. But "Yes, I see that" is not a habit or a permanent fact.

Re: Answer "I understand" or "I understood"
 

If you're talking about the car example, the answer would not be *I see it because as you correctly said, the present simple expresses a permanent event and this isn't. It would be I can see it. In English, when talking about sensory perception (with the verbs see, hear, smell, feel, taste) we nearly always use can :
Speak up! I can't hear you. / I can feel something crawling up my leg! /From my house in London I can see the River Thames. / I can smell something burning! / What did you put in this rice? I can taste apples.

On the other hand, when see is used to mean understand, then the present simple is fine because "understanding" is a permanent event :
A : I'm sorry, but I won't be able to help because I have to visit my grandfather in hospital.
B : OK, I understand. or OK, I see.

Re: Answer "I understand" or "I understood"
 

"I can see" also is the present simple tense. That's why I'm confused. However, your answer can solve this ploblem.

How about in the "past" case?
For example:[I saw that blue car in the last 10 minutes.]
My Friend: A) Can you see that car?
B) Could you see that car?
Me:A) Yes, I can.
B) Yes, I could.

Can I use A or B or both?

Thank you for answers. It seems to be that I've asked too much. :p

Re: Answer "I understand" or "I understood"
 

In the present, as I said, can is nearly always used - we express the idea as relevant to our ability to see, hear etc - to avoid the problem that the present simple expresses permanent events and therefore can't be used. However, you're right that it's different changes in the past. Then it depends whether 1) you're just talking about the event or 2) really talking about your ability to see the car.

1) A : Did you see the red car that was parked in the car park this morning? It was a Ferrari I think.
B : Yes, I saw it when I came in.

This is a past event and the past simple expresses past events -so here there's no conflict and you can use it.

2) It was so foggy when I drove to work this morning that I couldn't see the white lines on the road. = it wasn't possible to see