if I want to say "we are big", when "we" is a mixed group of males and females, which gender do I use?
Pronouns in czech have to agree with nouns in gender. Velký is male, velká is female, velké is neutral, velcí is plural male, velké is plural female and velká is plural neutral. Etc.
This is genders again. Sticking to Nominative case, "velký" is the masculine singular form, "velká" is feminine, "velké" is the neuter form. In plural, masculine animate is "velcí", masculine inanimate and feminine are both velké, and neuter is "velká". You use whichever form agrees in gender and number with the noun.
In the pronunciation of the letter "c", the "t" sound certainly drowns out the "s" sound here. Does that have something to do with the diacritical mark above the "i"?
I would say no because the literal translation of 'velci' is big/large.
trying to translate/associate it with 'great' is an abstraction that would require quite a lot of context to support it in English.