How does a woman combine two prayers, what is the correct intention she should have for that, and how are the prayers of shortening (qasr) and combining (jam') performed during travel?

The basic rule is that it is impermissible to combine two prayers except in specific cases, and there is no difference between a man and a woman in the manner of combining them.

For Jam‘ at-Taqdeem (combining and praying early): The first prayer is performed, then the second immediately after, without any interruption. The intention to combine must be made when beginning the first prayer with the takbirat al-ihram.

For Jam‘ at-Ta’kheer (combining and praying late): The first prayer is delayed with the intention of combining it with the second, and both are prayed together during the time of the second prayer, in their proper order. It is required to have the intention of delaying the combination during the time of the first prayer, such that there remains enough time within the first prayer’s period to perform it.