GMAT Strategy

Is there any penalty for spending more time on a question in the GMAT exam? Also, Is there any penalty if we don't press the submit button for the AWA section or any other section in the time limit despite being on the last question of that section?

No, there's no penalty for spending more time on a question. Spending an average of 2-minutes per question is typically recommended, but you may spend less time on easier questions and slightly more time on more challenging questions.

You have to try a few different ways and do what works for you. The 2nd time I took the test I listened to other people by moving on after two minutes, kept being so focused on timing that I just coudn't focus on the questions- your always worrying about the time - I got a 38 in quant that time.
I retook the test 3 months later without studying between the 2 attempts. This time I relaxed, said screw the time, and took the test as if I was relaxing on a beach- I got a 48 in quant. I also had to guess on a ton of questions and had around 8 minutes left for the last 10 questions... do what works for u !

Very true - timewatch can build anxiety. A recommended strategy would be to eye the timer after every 10th question.
Quant - Q10 (25th min), 20 (45th min), 30 (65th min), and 37 (75th min), this is to give a good bit of time for the first 10 questions, as they can take you to a bench mark score.

Verbal - Approx 7 mins for an RC, so typically 30 mins for RC's, 20 mins for CR, and 25 mins for SC's. As you will not know when each type of question arrives. You can only watch time for an RC passage and ensure to complete it within 7 - 8 mins.

Good Luck.

Shabbir