Is Zakat obligatory on a sum of money designated for investment upon the passing of a year (Hawl), and how is Zakat paid on land that was purchased with a portion of this sum six months ago?

Yes, every individual must pay zakat on their share of mixed funds and land if it is for trade, provided that their share reaches the nisab, even if by combining it with other zakatable wealth they own, and that a hawl (full lunar year) passes over it. The wealth of partners is not combined to complete the nisab, because mixing (of ownership) is not considered for zakat except for grazing livestock according to most scholars. And whoever's share does not reach the nisab, no zakat is due on them.