Yes, the phone must be rooted in order to install MIUI ROM. In terms of the warranty, if it is direct warranty under SIS (So-called "Original" warranty), the phone will no longer under warranty once rooted.

Technically speaking, once the phone is unroot back to its original state (By installing the original ROM), you should be able to claim warranty as there will be no track on the phone that it had been rooted before.

MIUI ROM is one of the many custom ROMs out there, personally i would say it is still a good ROM if you can live without Sense.

Since the phone is already rooted, you can always flash to other custom ROM if you found that MIUI is not suit to your usage and preference.