If there is a decision in your favor eventually, you will be paid only for those weeks for which you have signed, and in which you have met all requirements of the law.
If the original determination is in your favor, you may begin to receive benefits. You should be aware, however, that if the determination is later reversed (following a successful appeal by your employer, for instance), you may be required to repay that amount to DUA or to have your overpayment offset against any future benefits.
If you find new employment while you are waiting for your hearing, it will not affect your appeal. You should stop signing if you are employed full-time and continue to pursue your appeal for the weeks you were unemployed. If you begin part-time work, you should continue to sign. If you are eligible for partial benefits after you win your appeal, checks will be mailed to you.