For 2. you can't enter custom pairs for auto-complete (in the Auto-Insert section) with two characters. So this is not possible without a plugin. If I find one, I will update my answer.
Please note that using < and > or any other similar pairs will break other auto-complete functionality (including the auto-close html tags). This is certainly bad, because it would be nice to have both <> auto close and html tags auto-close.
Regarding auto-closing html tags, for me only having html as the language didn't do the trick.
(This answer is incomplete, but is too large for a comment given the images.)
Changing the auto-complete preferences, as below, worked:
I use Notepad++ v6.5.2
If you are editing a PHP file and want it to auto-complete the HTML tags, in addition to turning on "Auto-insert HTML/XML tags" in Preferences, you have to change the programming language to HTML while editing that file.
In Notepad++, go to the Language menu, and find HTML and click on it.
This will set the file's language to HTML so that auto-complete tags will work in a PHP file.
Even with the language set to HTML, it still highlights anything in <?php ?> tags as PHP code, and it does not affect auto-closing of brackets, if you have that enabled.
You must have Auto-Insert html/xml close tags on, as mentioned in Noha's answer.