Can a rank 2 guild use the guild armory, guild wardrobe and guild storage chest if I buy them with guild gems? And can a rank 2 guild even buy those things? Thanks for any help.

No you can't buy any of those till your guild reaches the correct rank.

3 for Storage Chest
4 for Wardrobe
5 for Armory

Even if you attempted to try and buy those it would tell you can't