GNAV...

Let me explain with an example.  The Laser has no forestay and you can tension up the kicker all you like and yet still lift the entire rig out of its socket in that condition.  However try applying the kicker to an Enterprise and then if you can release the forestay - you'll find the rig promptly falls backward out of the boat!

No don't try it on an Enterprise you'll break it but I think you'll get my drift - a kicker anchored to the mast does not increase forestay tension and one anchored to the boat does.

Now here's something to get your head into - what happens when the boom is eased out over the side of the boat?

Ummm.  Yes, the hounds will move down, but also aft. So, shround tension will decrease as the triangle of Shroud(s), mast, shroud/chainplate has changed shape (hounds are nearer the shroud chain plates).  Agreed ?

Thus mast must be bending aft (and comppessing to an extent as it is bending, and also (maybe) moving forward depending if our boat has lowers or not) Agreed ?

Thus, as the mast is bending (Aft and Down) the forstay attachement will be moving down a small amount but aft a too.  Agreed ?

Now if you you remember you school maths, the movement aft (on the curve) of the hounds will be much greater than the movement down (on the same curve untill you get past 30 degrees of movement / bend).  Thus, even if we allow a little bit of extra 'down' component for mast compression, I still believe that there will be a larger (Attempted) movement aft than down and so the forestay will be attempt to streached more.   Consider the triangle Deck / Forestay / Mast.  Which will strech or compress most ?

Deck - None (we hope)

Mast - Compresses a little and also bends

Forestay - streaches little, so incresed tension in Forestay

QED.   

Depends on whether the base of the mast is a fixed joint or a pinned joint. 

If the mast falls over without the rigging up, I would say it is a hinged connection.  Therefore if the kicker is attached to the mast - or even to the mast step as on Matt's Contender - its only action is to bend the mast.  The only action on the forestay tension will be as a result of the change in the mast bend.

Only if the kicker is anchored well below the mast step, or if the mast is made to have a fixed base by using lowers or a strut, will there be a direct effect on the forestay tension.

But, when the boom goes out, the kicker tries to bend the mast sideways not fore and aft.  So if it had a fixed base, easing the main would also reduce the forestay tension.  Talk to a Cherub sailor and they will say that the main point of lowers is to stop the mast bending sideways when the main is eased, the strut deals with fore and aft bending.