-Since when do Poles call their country "Polska"?
since 11th or 12th century most probably
Has there ever been a time when it was called something like 'Lechia"?
it was never called Lechia since Lech was a legendary ancestor of Poles and not a name of any tribe that later came to live in Polska (after the Polans conquered their neighbours)
Has there ever been a period where the Polish language/dialect was called something based on this 'Lech-' stem?
you just reminded me that there must have been a tribe of Lęch people who became known Ljach(y) in Ukrainian - but the tribal name expired as the Lęch (perhaps) Lędzianie) submitted to the Polan's state - the common language of Poland was never called Lechicki though
-Since when do Poles and/or outsiders view Polish as a independent language instead of a dialect?
since quite early - there were serious differences among Slavic Languages as early as 9th century (the loss of nasal vowels in most Slavic languages and kept in the Lechitic family (Polish dialects, Pomeranian dialects, and some Polabian dialects) - serious differences between Czech and Polish existed as early as 10 th century (Czech h instead of former g and a couple of various other differences)
-Are Legia (as in Legia Warschau) and the personal name Lech related to each other?
no Legia is unrelated to Lech - Legia is related to legion and is a Latin borrowing into Polish