Query 2 and Query 3(i.e. SELECT * FROM `tablename` WHERE 1 and SELECT * FROM `tablename` WHERE 1=1) mentioned in the question are the same in MySQL.
Functionally, if you see Query 1 i.e.(SELECT * FROM `tablename`) is also the same.
'WHERE 1' syntax is not standard therefore, it will not work in other dialects.
We can add 'WHERE 1' or 'WHERE 1 = 1' syntax hence, because WHERE conditions can be easily added or removed to/from a query by adding in/commenting out some "and ..." components like this:
FROM `tablename` WHERE 1=1
--AND Column1 = 'Value1'
AND Column2 = 'Value2'