How many times can we perform Umrah when we go to Hajj first time? and can we perform Umrah for our marhoom father when we go to Hajj first time?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Here is a detailed answer of your specific question.
If the person does his Hajj al- Qiran (combining Hajj and Umra) or al- Tamttu' (combining Umra and Hajj with a break in between) his reward includes both the reward of a Hajj and the reward of an Umra. So he does not, in this case, need to perform an independent Umra after the Hajj. But if the person does Hajj al- Ifrad (Hajj only) it is lawful for him to perform an Umra right after finishing the Hajj. However, he should not do the Umra in the same travel more than once as this has not been reported from the Prophet nor his companions who were undoubtedly keen on doing good acts and getting much reward.
As for doing Umra on behalf of one's father one's mother or any other person, it is unlawful if that person is able to perform it himself or if he has already performed it in his life. But if the person has never performed Umra and was unable to perform it or was dead, it is lawful for you to perform Umra on behalf of him after having performed it yourself.
Allah knows best.