Is it permissible to propose to a woman whom a colleague saw and rejected? And would marrying her be Islamically valid, or would it be flawed due to the colleague having seen her?

If the woman is pleasing in character and religion, there is no objection to proposing to her. Your friend's mere glance at her is not an impediment to your marrying her. The prohibition against a man proposing after his brother has proposed is until the first suitor abandons his proposal or gives permission, and this is what occurred with you. Therefore, if you are sure of her religiosity and character, you should perform Salat al-Istikhara and then propose to her.