Is it normal to hold hands if i'm not in a relationship with her yet?

She's interested if she's going on a date with you. You should definitely test the waters and try and hold her hand. Dates are about getting closer. Holding hands in innocent enough and it will give you a good reading on her feelings about you

Why not? Just move slowly and see how she responds. She obviously has interest in you. I think there's nothing wrong with moving at whatever rate you are comfortable & she is accepting of it. As long as you are both single and aren't dating other people, you shouldn't feel any apprehension or guilt - new people & relationships are exciting. If it turns serious, just remember to stay sweet & hold on to the initial feelings of excitement so you remember every real, mature, worthwhile, successful relationship takes work, respect, understanding, openness, trust & appreciation. Best of luck.

If both two agree. I do not find any issue.

Do it in a friendly, inviting way, make it seem natural, like offer her ur hand after u met up, like a quick sideways hug and then offer her ur hand, nahhh mean cuz?

It's normal to take your cues from the girl. If she'll take your hand while walking, then perhaps an arm over the shoulder would be OK. If not, take it at her pace and be patient. Remember, she's just as nervous and unsure as you are.
I would like to suggest that you ask her out to a comedy club instead of a dinner/movie thing. One, it's more unique and food is available. Second, the comedians are doing the talking, which saves on the awkward first date conversation. Lastly, women love a man who makes them laugh, has a good sense of humor and is a bit different.

I think that's normal, if you don't she might think you don't see anything in her.

Yeh, do the old *yawn; arm around the shoulder...so subtle she doesn't even notice* technique. No seriously, don't even worry about it... If you're consciously thinking about it, then it will almost definitely feel a bit forced and unnatural. Really be more subtle and don't automatically go to hold her hand or put your arm around her, that might be weird.