A good, engaging webinar stimulates lots of audience interaction. With any luck, you'll have more questions than you can get to within the allotted time slot. What is the best practice for handling those leftover questions?
Surprisingly, I don't care. Do whatever is most appropriate, practical, and cost effective for you. Respond to individuals by email. Post an FAQ in a public location. Pick a few of the most interesting or most commonly asked questions and respond to those. Ask people to email you their question if it is important to them and they really want an answer. Or just dispose of them and accept that questions were only being used for in-session handling up to the time available.
The important thing is to make your choice BEFORE the webinar starts and to clearly let your audience know at the end of the session how you will be treating the extra questions.
It is very frustrating for attendees to be left hanging, unsure of whether they should expect a response or if they are expected to take an action to find the answers (and when those answers should be available). Part of your duties as an effective webinar host is to set and manage expectations. Speak with your presentation team ahead of time and decide who will deal with unanswered questions, what the response mechanism will be (if any), and what the time commitment is for finishing responses. If you waffle about this at the end of your webinar, you lose the impression of being a well-prepared, professional business operation. Don't make that mistake… End strong and confidently!