are they genetically linked to other sri lankans?
Yes,  genetic studies indicate that they are closely related to the Sinhalese ethnic group in the island.
Sri Lankan Tamils
Although Sri Lankan Tamils are culturally and linguistically distinct, genetic studies indicate that they are closely related to the Sinhalese ethnic group in the island. 
how many tamils are there in sri lanka 70% since how long have they been living here? Sri Lankan Tamils have a very long history in Sri Lanka and have lived on the island since at least around the 2nd century BCE.
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Sri Lankan Tamils [SEP] Introduction
According to the anthropological and archaeological evidence, Sri Lankan Tamils have a very long history in Sri Lanka and have lived on the island since at least around the 2nd century BCE. Although Sri Lankan Tamils are culturally and linguistically distinct, genetic studies indicate that they are closely related to the Sinhalese ethnic group in the island. The Sri Lankan Tamils are mostly Hindus with a significant Christian population. Sri Lankan Tamil literature on topics including religion and the sciences flourished during the medieval period in the court of the Jaffna Kingdom. Since the beginning of the Sri Lankan Civil War in the 1980s, it is distinguished by an emphasis on themes relating to the conflict.