improving isearch

Question

1. I wonder if I can disable the 'failing overwrapped' warning in the minibuffer and directly wrap around instead if I do a search?

Does anyone know how to facilitate this?

2. Also there is a slight delay in highlighting occurrences of the search-for expression, can I decrease this as well?

3. Finally, how can I invoke custom function upon a key combination, only if Isearch is active?

Specifically, I want to invoke

  (defun contrib/isearchp-remove-failed-part-or-last-char ()
    "Remove failed part of search string, or last char if successful.
Do nothing if search string is empty to start with."
    (interactive)
    (if (equal isearch-string "")
        (isearch-update)
      (if isearch-success
          (isearch-delete-char)
        (while (isearch-fail-pos) (isearch-pop-state)))
      (isearch-update)))

if I hit <backspace> during Isearch.

Answer 1

For quick direction change and wrap around you can use the following:

(defun isearch-repeat-forward+ ()
  (interactive)
  (unless isearch-forward
    (goto-char isearch-other-end))
  (isearch-repeat-forward)
  (unless isearch-success
    (isearch-repeat-forward)))

(defun isearch-repeat-backward+ ()
  (interactive)
  (when (and isearch-forward isearch-other-end)
    (goto-char isearch-other-end))
  (isearch-repeat-backward)
  (unless isearch-success
    (isearch-repeat-backward)))


(define-key isearch-mode-map (kbd "C-s") 'isearch-repeat-forward+)
(define-key isearch-mode-map (kbd "C-r") 'isearch-repeat-backward+)

By binding the keys in isearch-mode-map those bindings are only used when isearch is active, you can do the same with your contrib/isearchp-remove-failed-part-or-last-char command.

As for the delay question, you need to search for the variable for this setting. You can use apropos-user-option, apropos-documentation or just describe-variable (+ maybe using a completion framework of your choice) to find isearch-lazy-highlight-initial-delay which is obsoleted by lazy-highlight-initial-delay (as you can read in the docstring).