Does he live in Minas Tirith?

He's had control of Orthanc since 2755 if I recall correctly.

Saruman has had the keys of Orthanc since 2759 TA and has dwelt there, but Isenguard itself was still a stronghold of Gondor protecting the Fords of Isen. The stronghold gradually declined and men of Dunland moved in to the area. By 2946, Isenguard is probably under the influence of Saruman to the greater extent. In 2953, Saruman claims Isenguard as his own personal stronghold, breaking with Gondor completely.

No. The division (=difference of forces in control) between the tower of Orthanc and the Fortress of Isengard around it only had a meaning during the time of the dunnish occupation (c. TA 2700-2760), when the tower was locked and the keys in possession of the Stewards, while the fortress was in dunnish hands.
After Saruman arrived (TA 2759/60) he was given the keys of the tower and control of the surrounding fortress. He stayed there ever after, not counting temporary visits to other areas.

After Saruman moved in, he had full control of the whole complex and surrounding lands, lasting ca. 260 years.

EDIT: See also this thread for a very similar question.

Cheers
Tolwen

Thanks guys!