Based on the experiments from JasonC and the answer from Aurora0001 on How exactly are Area 51 beta stats calculated?
I'm pretty confident the formula for Answer Ratio is:
(sum of answers not deleted) / (number of questions with at least one answer that are not deleted).
And this SEDE Query
select cast(sum(answercount) as float)
/ count(*) [Answer Ratio]
where posttypeid = 1 -- Q
and answercount >= 1
or closeddate is not null -- only open questions
would tell you today the answer ratio for Hinduism.SE is 1.6097222222222223 which is way closer to 1.6 that is mentioned on Area 51. I hand checked around 10 other sites against this query and they all line up so I assume that the SEDE refresh on sunday should bring those numbers back in line, at least that is what I hope.
Now we can answer your specific questions:
Answers are deleted due to lack of sources & low quality. Are those counted in the AR, which has to be minimum 2.5 as per the area 51?
No, they are not. It makes no sense to account for content no one is going to see
Do votes to existing answers matter, for the calculation of the AR?
No, votes do not matter although questions without answers that have a score above 0 are considered unanswered and as such show up on the unanswered tab of the site, bringing those questions to the attention of possible answerers.
Does closing a Qn as duplicate, increase the AR?
e.g. A Qn has 3 answers & its linked dupe has 2 answers. Will the AR for just these 2 Qn-s be 2.5 or higher?
No, closing as a duplicate has no effect on the ratio, AFAICT.
How to increase AR for this site?
Post more answers, if possible multiple answers per question.