I was able to find solutions on the web for your other questions on selecting multiple emails and rule creation but this one seems to be a known problem with Outlook on Web. I've found a few similar questions and feature requests from Microsoft.
I've tried to select multiple emails from my own search results. I've did somehow manage to do it but can't exactly put my finger on the proper process. It's a little bit cumbersome but this was the only way that I was able to select multiple items (or all items) from a search result.
I'll try to write down the process.
Search your string
Select the first few 4-5 emails all together from the search results by using the Shift key
Scroll the list down just for a few emails (Something like 10-20-30. More than that does somehow break down the process)
Select an email from the scrolled list by pressing the Shift key
All the emails between the first group and the selected email will be selected. You can further scroll the search results and select more emails with this method by considering the 10-20-30 item scrolling limit. Don't be alarmed if you've accidentally scrolled too much down. If the selected email doesn't refresh the total selected email count you can always scroll back up and select another mail. The total selected email list won't reset.
You can do all the possible actions on this group from the central menu or from the right button menu
Under your last folder (before Groups) click on "More".
This will take you to the Folders side window. On top you will see your "Favorites" folders, under that will be your login name and the same list of folders as are shown in "Favorites".
Right-click on the folder that you want to rename that is listed under your name.
You will then see the option to rename. Once you go back, the folder is renamed.
Best Answer
I don't think you can. There are eight pages of negative comments from people having exactly this problem here.