From the insurance perspective, my advice* is to fill in the questionnaire as accurately as possible. Duty of disclosure and the principle of utmost good faith are paramount, even for group life.
If you are asked to send it back through HR, you are within your rights to ask to send it back directly.
Your group life cover is probably subject to a "Free Cover Limit" where no medical underwriting is required and no further requirements/loadings (apart from any standard age-related premium factors) will apply. If you are above the FCL, you would have to undergo further underwriting.
If it doesn't affect your job, you do not need to disclose any medical information to your employer. Of course, this is up to you. It is also ok to tell your employer you need time out of the office for medical care (without disclosing the practitioner and/or diagnosis) as long as you take leave/exeat/work the hours back (depending on your company). This can be for regular care (eg appointments with a therapist) or for once-off appointments.
What I will also advise* is if a episode/relapse will definitely affect your ability to do your job, is to tell your boss and HR. It isn't always possible to identify (by yourself) when a condition (mental or otherwise) might impact our work.
* Insert standard internet forum advice from a random person disclaimer
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