Question mark right after the domain: domain.com/?z=this

Since index.php etc. are automatically detected as the default page and don't need to be specifically spelled out, it's possible to refer to dynamic pages without the index file name.

E.g. domain.com/?z=this instead of domain.com/index.php?z=this

Does this, however, confuse search engines? Google and Yahoo are my main concern.

You will find that what you describe isn't a problem, web spiders will always locate the index.php or html pages and then index all the files that link from that page so it wouldn't be a problem at all.