'He is yet young' means the same as 'he is still young'. Answer should be accepted.
No, these are optional. Review the Tips and notes of the To Be Or Not To Be, Singular skill.
When the verb is a form of "to be," "still" should appear immediately after it. From the Cambridge Dictionary: We usually put still in the normal mid position for adverbs (between the subject and the main verb, or after the modal verb or first auxiliary verb, or after be as a main verb). "To be" is the main verb in this sentence. Link: https://dictionary.cambridge.org/grammar/british-grammar/adverbs-of-time-and-frequency/still. In the future, perhaps other options will be considered.