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I am playing in a tournament and so we are using the victory points rules on page 300 of the rulebook.

Units destroyed
At the end of the game every unit that has been
destroyed is worth an amount of VPs equal to its points
cost (including the cost of all its extra wargear, vehicle
upgrades, etc). Units that end the game falling back or
off the battlefield count as destroyed.
For example, a 260 point Land Raider would be worth
260 VPs to the opponent if he managed to destroy it by
the end of the game.

Units at half strength
At the end of the game every enemy surviving unit that
has lost half of its initial models or more is worth an
amount of VPs equal to half its points cost (including the
cost of all its extra wargear, vehicle upgrades, etc),
rounded down. In the case of units that start the game
as a single model (independent characters, monstrous
creatures, etc), they are worth half their points cost in
VPs if they have lost half or more of the Wounds on their
profile. In the case of vehicles, they are worth half their
points cost in VPs if they are suffering from the effects of
any Damaged result at the end of the game.
For example, a squad of Space Marines starts the game
at 10 models strong (costing 190 points) and ends the
game with only 5 models left. Such a squad is worth 95
VPs to the opponent.

Retinues
Some Codex books allow you to field characters
together with a special unit that they cannot leave
during the game (which is normally called a ‘retinue’,
‘bodyguard’ or similar). Where this is the case, the
character counts as an upgrade character until all of
the other members of this unit are killed, at which
point it starts counting as an independent character
and it will do so for the rest of the game.

I have the following unit:

Shas'el - 2 shield drones 110pts
2 Bodyguard 164pts

a) I lost 1 bodyguard.

i) I have lost half of the bodyguards. I give up 82pts.
ii) I have not lost half of the unit. I give up 0pts.

b) I lost 2 shield drones and 2 bodyguard.

i) I have lost the bodyguards and half of my character. I give up 219pts.
ii) I have lost half the unit. I give up 137pts.
iii) The drones form a unit with the character, thus fall under the retinue rules. I have lost my retinue, so the character is now an independent character. I have lost 194pts worth of retinue. I give up 194pts.
iv) The drones form a unit with the character, thus fall under the retinue rules. I have lost my retinue, so the character is now an independent character. I have lost 164pts worth of retinue. I give up 164pts.

c) I lost 2 shield drones.

i) I have not lost half of the unit. I give up 0pts.
ii) I have lost half of my character. I give up 55pts.
iii) I have lost half of my retinue. I give up 97pts.

once the character is given a bodyguard everything in the unit becomes one unit, so if commander + drones + bodyguards is below 50% you will give up half points for all those things, otherwhise it's 0 points total. So applying this to your specific questions.

a) ii.

b) ii.

c) i.

I agree. The wording is clear: if the unit starts with more than one model, VPs are given up if that unit loses half of its total models. So I agree with Drunkenspleen in all cases as it is the RAW.

The tournament organizer has ruled it the same.