Why is it ваша here? Is подорож feminine?
Yes. For some words you just need to memorize their gender
I also know «подоріжжя» and beautiful word «мандрiвка». What is the difference between them all?
Подоріжжя is a dialect word (never actually heard someone using it). Подорож and мандрівка - no difference
Good learning here, but in English we would say "How was your trip?" so I'm not understanding whether this Ukrainian sentence is really past or present.
Just guessing here, but the above question might be valid if you were still in the midst of your trip. That said, I understand your point.
Either "is" or "was" are accepted here. "How is your trip?" can be asked while the person asked is on the trip.