I think you are English native speaker who understands most of Polish concepts, is there any difference in English? if so what is that difference? would you translate "large bathtub" to "duża" or rather "wielka" ( very big, great)? If there is no difference report. Creators may have not thought about it.
"large" and "big" are very close synonyms and I would translate both has "duża" - in my mind "wielka" would be larger than large - perhaps enormous or yes great.
Yes, double letters are pronounced as double letters. Other examples include "inny" (other) and "miękki" (soft) for instance.
Yes, the pronunciation is correct. As a rule, you read what's written, so if you see two 'n's you need to pronounce them both.
Maybe I'm being picky but in England we don't say "bathtub", we simply use "bath"