which language was it written in?
Sanskrit
Chalukya dynasty
Famous writers in Sanskrit from the Western Chalukya period are Vijnaneshwara who achieved fame by writing Mitakshara, a book on Hindu law, and King Someshvara III, a noted scholar, who compiled an encyclopedia of all arts and sciences called "Manasollasa".

which dynasty succeeded the chalukyas in western india UNANSWERABLE when were they in power? Between the 6th and the 12th centuries and what was the extent of their empire? Southern and central India in Karnataka, Maharashtra and coastal Konkan. can you name some important texts composed during this period? Mitakshara, Manasollasa, Prabhrita, Chudamani who composed the first one? Vijnaneshwara can you name some places where remnants of their architectural grandeur are extant? Nearly a hundred monuments built by them, rock cut (cave) and structural, are found in the Malaprabha river basin in modern Bagalkot district of northern Karnataka; Lad Khan Temple which deity is the last temple you mentioned dedicated to? UNANSWERABLE who composed the second text you mentioned above? King Someshvara III
wiki:13894195
Chalukya dynasty [SEP] Literature
The rule of the Western and Eastern Chalukyas, however, is a major event in the history of Kannada and Telugu literatures respectively. By the 9th–10th centuries, Kannada language had already seen some of its most notable writers. The "three gems" of Kannada literature, Adikavi Pampa, Sri Ponna and Ranna belonged to this period. In the 11th century, Telugu literature was born under the patronage of the Eastern Chalukyas with Nannaya Bhatta as its first writer.