you can remove ".php?" from the url, if you are on Apache webserver.

you need to install plugin local files editor and write some new config according to specs
[Github] Piwigo file include/config_default.inc.php@L589-L624

as you can see in the specs also is possible to remove the numeric ID from tags or categories.

i don't think is possible to make "index" or "picture" disappear. it has been discussed many times on the forum.