"The girl has everything."
Translation:У девочки есть всё.
No, you should not omit "есть" here.
Mostly, you omit "есть" when you focus on the object one has, not on the fact of having it. It may also mean that someone is holding something (not necessarily owning it). Like: У девочки яблоко, а у мальчика груша - The girl has an apple, and the boy has a pear.
Yes, I am having this problem throughout the course. In general, the transliteration option is working well and systematically and allows one the choice of whether or not to use the punctuation marks for soft signs, etc.
However, this one word, есть, seems to refuse to transliterate into any form. I've tried it with and without the apostrophe for the soft sign and have also tried the 'yest' variant, but still no luck.
Fortunately, this word seems to be used less frequently later in the course so it is not too much of an issue.