Modern fax machines use "computers" to transmit text, since computers use the Internet, which remains the fasted and simplest way to transmit information in the modern world.
This is a simile as it compares two things using the word like. It compares her running across the grass to a cheetah chasing its prey, implying she is running very fast
There are many words that can match ecstatic, basically anything that means happy because ecstatic is just very happy, so words like joy, excitement, happiness, joyful, many words that have similar meanings, but I would need the part of the story if I needed to directly point out signal words for ecstatic.
