1- Any member with a rank that has land acquisition permission can purchase an entry of behalf of a FC (assuming they also have the gil).
2 - new members have a waiting period before they can be granted land acquisition permission or receive transfer of FC leadership. No permission, no ability to purchase an entry on behalf of a FC.
3 - a sprout isn't necessarily a newly created character but would still be subject to the waiting period for the necessary permission if a new FC member.
4 - They've said nothing to indicate FC eligibility to obtain housing is being changed from the current requirement of reaching Rank 6.
5 - The November Live Letter repeated that a member only needs to have a rank that includes land acquisition permission. There is no level requirement.
On your additional thoughts:
Someone leaves the FC after purchasing a FC lottery entry? They won't be able to purchase land if the entry is the winner because they'll no longer have land acquisition permission (the plot still has to be purchased even after an entry wins - ownership isn't automatically granted).
There's no reason not to allow FCs to demote players with lottery entries for the FC. They can always be promoted back if needed.
The entry holder is still the one who has to make the purchase because the entry is tied to their character, not the FC. The purchase can only be made for the FC because the ward will have the FC purchase designation (no "oops, I bought the house for myself by accident" unless they purchase the ticket in an individual ward in the first place).
I have no idea what would happen if someone tried to delete a character with an entry - might error?
All non-winning entries are 100% refundable. It doesn't matter if the FC wins a plot.
It will forever be a problem with the ward system - RMT has the resources to get around any restrictions by creating multiple service accounts to gain advantage. Too many restrictions end up causing more problems for legitimate players and FCs than obstacles for RMT.
But advantage is still not a guarantee of a win. Unless there's almost no one else entering, your chances of losing is still much higher than your chances of winning.