Learn Russian: У этой машины высокая скорость.

In Russian, when you are describing a specific quality or characteristic of something you have (like the fact that its speed is high), you usually drop есть. You would use есть mainly to state that the thing simply exists, as in У этой машины есть мотор (This car has an engine).

Why is it этой машины instead of эта машина?

The sentence uses the standard Russian "to have" construction, which requires the preposition У followed by the genitive case. этой машины is the genitive form of the feminine phrase эта машина.

How do we know the gender of скорость?

The noun скорость ends in a soft sign (-ь), which means it could be masculine or feminine. However, we can easily tell it is feminine here because the adjective describing it, высокая, has the feminine nominative ending -ая.

Could I use быстрая (fast) instead of высокая (high) here?

In Russian, speed (скорость) is traditionally described as "high" (высокая) or "low" (низкая), rather than "fast" or "slow". You can say the car itself is fast (быстрая машина), but its speed is high.