Suppose my buffer contains the text "x1yx2" right after point, and that
`isearch-del-char' is bound to DEL in Isearch mode.  If I type

   C-s y DEL x1

then I would expect the search to succeed: the cursor would first go
after "y", then return to the starting point of search after pressing
DEL – this is how `isearch-delete-char' behaves, anyway.

Instead, the cursor remains after "y" after pressing DEL, and the search
fails with the cursor after the second "x".  I have attached a patch to
fix this.

I have also attached a second trivial patch for an unrelated, very tiny
bug.

Best,
Augusto