Was the Abbey Road album recorded at Abbey Road Studios?

Yes, it was, during the summer and early fall of 1969. Despite the Beatles' promise to producer George Martin to work together "like the old days", they were fragmented and squabbling, and were largely only in the same room when they had to be. Martin worked around this by having different Beatles in different studios at Abbey Road, recording at the same time, with him and Alan Parsons going back and forth.

A playback session where the band worked out the final running order of the album (John Lennon had earlier demanded that George Harrison write more songs, to be placed between Lennon's and Paul McCartney's songs so they "didn't have to touch each other"; Harrison declined the idea) was the last time they were together at Abbey Road.