Learn French: Tu es sûr que c'est faux ? - Are you sure that it is false?

The circumflex accent on sûr (sure) is there to distinguish it from the preposition sur (on). Without the accent, it would be a completely different word!

Why isn't que shortened to qu' here?

The word que only drops its 'e' and becomes qu' when the following word starts with a vowel or a silent 'h' (like qu'il or qu'elle). Because c'est starts with the consonant 'c', the que stays whole.

If I am talking about a feminine thing being false, does faux change to feminine?

Normally, yes, the feminine form is fausse. However, when you use the phrase c'est (it is) to describe a general situation or previously mentioned idea, the adjective that follows is locked in the default masculine singular form, so it stays c'est faux.