I wouldn't mind seeing her again.

Question 1

I wouldn’t mind seeing her again.

Answer 1

You’re a single guy. You met a girl at your friend’s party and hit it off with her. Now your friend is asking what you think of her. You say this because you would like to go on a date with her.
I wouldn’t mind seeing her again.
I wouldn’t mind (doing something)
To “not mind” something means to be OK with it, or to not be bothered by it:

A: Sorry it’s taking so long.

B: No problem. I don’t mind waiting.

You use the phrase “I wouldn’t mind ___ing” when you want to do something, but you don’t want to seem too eager.

A: So… what should we do now?

B: I wouldn’t mind getting a cup of coffee.

In the example above, even if the speaker is really interested in this girl and excited about seeing her again, he probably wants to act cool in front of his friend.

The meaning of “I wouldn’t mind ___” can change depending on which word that you stress, though. If you don’t really want to do something, you can stress the word “mind”:

I wouldn’t mind going…”

This means that you don’t really want to go, but you will go if necessary.

see (someone)
There are multiple meanings for “see (someone”. One is to simply see someone with your eyes:

I saw her at the farmer’s market yesterday.

But you can also use the phrase “seeing someone” to mean “dating”. For example, if you’re interested in a person you can ask:

Are you seeing anyone?

This means, “Do you have a boyfriend / girlfriend?”

I’d like to see you again sometime.

This means “I’d like to go on another date with you.”

The expressions using “see” sound cooler and more natural than directly using words like “date”, “boyfriend”, “girlfriend”, and so on.
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The first question really depends on the person and what kind of personality they have. Some people might not bother being polite. But one way to politely praise a person you don’t like that much is:

She’s really nice.

The word “nice” is a really weak compliment, so people often use it to describe things that are good but not great.

One way to judge the nuance of “I wouldn’t mind ___ing” is where the stress falls in the sentence. When you stress the word “mind”, you’re actually saying that you don’t really want to do somthing, but you’re not 100% against it:

I wouldn’t mind(MİND kalın işaretli) going out with him.

This is how you would answer your friend who offered to set you up on a date with someone, when you don’t really want to do it. When you’re using “I wouldn’t mind ___ing” to express something you do want to do, put the stress on the “___ing” part:

I wouldn’t mind going out(Going out kalın işaretli) with him.

This is how the example in this post should be pronounced.