1) You don’t have to apply for a transit visa if you are eligible for a Transit Without Visa (TWOV) concession. The rules for TWOV are outlined here: http://www.ukba.homeoffice.gov.uk/sitecontent/documents/policyandlaw/carriers/ukvisarequirements.pdf
Indian citizens may not TWOV in general. However, it looks like you
meet the following exception:
TWOV is a concession which does not apply to nationals of the
countries shown above in red who need visas even when in direct
airside transit unless they are in possession of one of the following
documents:
…
(ab) a valid visa for entry to Australia, Canada, New Zealand or the
United States of America and a valid airline ticket for travel via the
United Kingdom as part of a journey from the country in respect of
which the visa is held to another country or territory;
So you should be able to TWOV.
2) You can do sightseeing.
Credit:stackoverflow.com‘
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