Should the husband perform the obligatory Hajj first, then perform Hajj on behalf of his parents who did not perform it? And is a woman's travel for Hajj with a group of women (through a company) considered as having a mahram?

It is obligatory for a husband to perform Hajj for himself first. He may perform Hajj on behalf of his parents later. Some scholars have stipulated that he must have performed Hajj for himself first. As for performing Hajj on behalf of another, there are several cases:

The first: The elderly person and the sick person with an incurable illness. It is obligatory for them to delegate someone to perform Hajj on their behalf, according to the majority of scholars.

The second: The sick person whose illness is expected to be cured. Hajj should not be performed on their behalf.

The third: Whoever dies having been obligated to perform Hajj but did not perform it. It is obligatory for their guardian to perform Hajj on their behalf from their wealth.