Honestly not sure because in this new era, Google lets you to create your search engine. I guess you can promote?
I'm sure for the first one, but there's no clue for the second in the TOS. Would you show the related part in the TOS on AFS?
You can encourage to use the search engine (Googel CSE) to find information on your site easily but do not encourage ad clicking.
You mean, I can say: "By searching in the search box below, you'll be searching this, this, this and this sites???"