I'm a PM on Confluence Cloud, and would like to learn more about your issues in (1). Can you send me an email to dlu at atlassian.com? I'll have some more specific questions, but if you have a video of your page loading experience you can send me that would be a great start.
I think (2) should only happen for a short period of time (a few minutes? I'm not sure) - the search index gets updated periodically. If the problem persists (deleted pages still appear even days later), let me know here and I'll ping a colleague.
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