e.g. - I hope you be/are fine during your travel
- I hope you be/are fine living in your new apartment
e.g. - I hope you be/are fine during your travel
- I hope you be/are fine living in your new apartment
Not really, no.
I hope you will be fine during your travels (or you'll is more natural)
is okay.
"Notice that the subjunctive is not generally used after verbs such as hope and expect, or after verbs that use a different syntax, such as want" -- Wikipedia and Kudos @Edwin
And
"In some examples, preserved in set expressions and well-known phrases, inversion may take place with non-auxiliary verbs: come what may; come Monday (etc.). "
-- Wikipedia