Is one who catches up with one or more rak'ahs of Dhuhr prayer before the entry of Asr time considered to have caught Dhuhr within its time, or must he interrupt the prayer and renew his ablution? And does the intention to interrupt Dhuhr prayer due to the entry of Asr time invalidate the prayer?

It is not permissible for a person afflicted with سلس (incontinence) to delay the prayer until its time becomes constricted, nor to exit it while performing it. This is because his purification (ablution) becomes invalidated thereby according to the majority of scholars. However, according to the Shafi'i and Maliki schools, it does not become invalidated. If he fears that the time will expire, he must begin the prayer. If the time expires while he is performing it, his prayer becomes void according to those who hold that purification is invalidated, and he must discontinue it, renew his purification, and recommence the prayer. As for the Shafi'i and Maliki schools, he continues with his prayer. Continuing the prayer while also repeating it as a precaution is good. If a worshiper intends to interrupt his prayer or makes its interruption conditional upon something, his prayer becomes void according to many scholars.