RE: A visit to ancient Jain temple which has 1000 yrs old idol

Yes OM symbol is relevant in Jainism.

There is no origin of Jainism as per Jain cosmology. It has existed since eternity and will remain till eternity just like this world. According to Jain cosmology, there is a time cycle of 6 "kaals" which moves in ascending and then descending order. First 3 are "bhog-bhumi" eras in which people don't perform any tasks and their wishes are granted by Kalpavrikshas. 4th is the era in which all Tirthankaras are born and preach Jainism. 5th era is the one we live in, in which no-one can attain nirvana. 6th and the last era is one doomsday come and everything is flooded. Then the cycle reverses and goes back to 1st era in reverse order.
Certain western historians, on the other hand, trace Jainism from the teachings of Lord Parshvanatha (23rd Tirthankara) who lived in 8th-9th century BC. It was then preached further by 24th Tirthankara Mahavira in 6th century BC. Various Indian historians on the other hand trace Jainism to as back as 3000 BC, i.e., upto Indus Valley Civilisation because of the seals depicting nude saints and bulls.