Depends on which department and your role.
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Yes, they can track in office days because you badge swipe to enter the building and in some cases the floor you work on(multiple swipes). Agree with commenter below that most flex positions are 3 days in the office but it varies by team. They are starting to come down on RTO defaulters. Most departments work on core hours, so ask if they have those; typically, most follow 9AM -3PM.
Do they track the number of hours in the office or is there any flexibility to leave early to beat the traffic etc?
Varies greatly by role and department. Generally speaking, most people who are not a full time telecommuter are expected to be in the office 3 days per week.