Can I date while the divorce is pending?
I suppose that you can, but my general advice is that you don't. Even though a divorce case is pending, you are still married. Having a sexual relationship while the case is pending is still adultery. Even in the abscence of any sexual contact, a dating relationship may be a strike against you in the divorce case depending upon the specific facts of your case.
If custody is pending, I certainly would be careful about your conduct with a "significant other." Many judges will not find such behavior proper, particularly if the person is being introduced to the children, spending the night while the children are there, or going out on social activities with the children.
The better course of action in this tpye of situation is to err on the side of caution. And, if you have a question about your specific situation and what would be appropriate, talk to your lawyer before taking action that could harm your case.