Not in case of security, but you get likely more trust from your visitors. Also might include some assurance thing you can use or advertise with. But I wouldn't say it has any bad influence if it's missing, as long as you aren't a payment provider or something like that.

Generally not unless you're in a business segment where trust is more important (e.g, financial services).

Depends on your audience. Do most know what it means? Do most even notice it?

Yes. In most cases, it means extra visitor trust.