Your second correction is exactly what we had in mind, each team has seperate votes. Here is a full example to make sure we all understand each other:
Team Red has 3 players (A, B and C)
Team Blue has 5 players (K, L, M, N, O)
Team Green has 1 player (R)
Team Black has 2 players (X, Y)
Each player has 10 voints to give out, max 5 to each team (standard voting rules)
Team Red votes like this:
A votes: 3 to Blue, 2 to Green, 5 to Black
B votes: 5 to Green, 5 to Black
C votes: 4 to Blue, 4 to Green, 2 to Black
Total for Red: 7 to Blue, 11 to Green, 12 to Black
Voints from team Red: 2 to Black, 1 to Green
Team Blue votes likes this:
K votes: 4 to Red, 1 to Green, 5 to Black
L votes: 5 to Red, 5 to Green
M, N and O chooses not to vote.
Total for Blue: 9 to Red, 6 to Green, 5 to Black.
Voints from Blue: 2 to Red, 1 to Green.
Team Green votes like this:
R votes: 5 to Red, 5 to Black.
Total for Green: 5 to Red, 5 to Black.
Voints from Green: 1 to Red, 1 to Black.
Team Black votes like this:
X votes: 4 to Red, 4 to Blue, 2 to Green.
Z votes: 1 to Red, 4 to Blue, 5 to Green.
Total for Black: 5 to Red, 8 to Blue, 7 to Green.
Voints from Black: 2 to Blue, 1 to Green.
Total results from Team voting:
Red: 4
Blue: 2
Green: 2
Black: 3
These voints are then added directly with the voints from the non-team voters and the teams are then given points as per the table in the Rules.
If a team gives equal votes to two teams, they will both get 1 voint (This is not in the rules yet, but will be added)
As for mandatory voting, you have a point. This will also be added to the rules.