Everyone can edit all pages. You can edit a page by clicking "Edit" at the top. Edit contents will be formatted according to the Formatting Rules.
In the Sandbox page, you can freely experiment with making whatever edits you'd like.
From an existing page (for example, the Sandbox page), if you enter WikiName(mixed-case) or BracketName(enclosed in [[]]) somewhere on the page, a "?" link will be added there. Upon clicking the link, the new page editing screen will be displayed, within which you can edit the page as normally (i.e. for an existing page).
This denotes when the link in question was last changed. For example: (3m) = 3 minutes ago, (5h) = 5 hours ago, (2d) = 2 days ago.
Edits and additions to pages are anonymous. For clarity and certainty, you can always "sign" your edits by including your name / userpage link. -- hogehoge (like so.)
That's just how it be on a wiki. Anyone, anywhere, can rewrite/overwrite content, but repairs can be done. PukiWiki has the ability to create regular backups, from which it is possible to restore previous versions of pages.
Editing is performed based on the page's state at the time of editing. If someone else makes changes to a page while you're editing it, worry not - PukiWiki handles comparing timestamps of the updated and original pages to ensure compatibility. In the event of editing conflicts, it may help to reload the page and repair edits accordingly.