One of the best things about reddit was looking for answers or other users with the same problem as you, and since Google didn’t really help with that anymore and instead insisted on giving you business results, the best practice was to put your search terms in followed by ‘reddit’ and you’d find your answer.
They can. For Mastodon there’s an option for “Opt-out of search engine indexing” which adds a “noindex” tag to your profile which Google respects. Not all indexers respect the tag however and “noindex” data isn’t federated which can cause your replies to show up: https://github.com/mastodon/mastodon/issues/22047