I totally agree about the first two items on your list - particularly the second one.
Every time I need to search backwards, or perform a case sensitive search (etc), I have to remind myself to turn the switch off again before I perform an unrelated search and get the wrong result! When I am searching for a string, my mind is on the subject matter - not on the quirks of the search box.
Probably the simplest answer would be to add a few extra search buttons with no history - ‘Search forwards’, ‘Search backwards’, ‘Search for whole word’ etc. However anyone who really wants to configure the search box with different defaults, should have to take some special action.
I also wish the search box would echo any shortcut keys it does not explicitly use back to the active window. As it is, when the search box has focus, the shortcuts do not work.
It is a shame the search box is as it is, because otherwise it is so powerful.
David