[Sternenwind]

What happens with the fireball after the target evaded (succeeded to dodge) it?

[farothel]

A fireball goes off in an area chosen by the mage.  Everything in that area gets a chance to dodge (if it can move of course) and those that don't get the damage.  Then the fireball is gone, as it's a flash effect (it appears, does its thing and dissapears in one IP if I recall correctly).

[Lucean]

Completely unrelated to the question, but knowing SR5 and then rereading AoE in SR4 is revealing ...
You don't need to allow the target a chance to dodge at all.

p. 183 SR4A:
A metahuman spellcaster can target anyone or anything she can see directly with her natural vision.
Some spells target areas or points in space; in this case the caster must be able to see the center of the area affected. All visible targets within the area are affected; area spells can affect more than one target at a time. The base radius for all area spells is the Force in meters. Area spells affect all valid targets within the radius of effect, friend and foe alike (including the caster).
p. 204:
Indirect Combat spells are treated like ranged combat attacks; the caster makes a Spellcasting + Magic Success Test versus the target’s Reaction.
The spell traverses the distance between the caster and the target near instantly, but travels over the physical or astral plane to do so only to take effect when it “hits”. Hence, Indirect Spells are handled as ranged attacks and require a physically solid target or astrally active target to hit.
As they travel down the link to the chosen target such effects may be impeded by physical obstacles or mana barriers. They may impact transparent obstacles (such as glass) and do not “bounce” off reflective surfaces used for line of sight. Instead the spell takes effect at the point of contact with an obstructing barrier.

So just target the ground or a wall in the vicinity of your enemies and they have no chance at all to dodge. The ground/wall/whatnot should be at Reaction 0, so hitting would be easy. Since the spell goes off when it hits something ...

Grenades have it the same (p. 155)
To determine the grenade’s final location, first choose the intended target. Make a standard ranged attack test using the attacker’s Agility + appropriate combat skill (Throwing Weapons or Heavy Weapons), opposed by the target. If targeting a location, treat this as a Success Test instead.

I like SR5

[Sternenwind]

Next:

You target something next to someone and this someone is protected by counterspelling.

[Lucean]

SR4A p. 185
When a protected character is targeted with a spell, she rolls Counterspelling dice in addition to the appropriate attribute (Body or Willpower) for the resistance test.
So technically one could argue that Spell Defense doesn't work against location targeted indirect aoe-spells. On the other hand we have a resistance test mentioned, which would be the next step after launching the spell.
So while Spell Defense would not be able to do anything against the casting, it would aid in diminishing the effect of the spell by giving more dice to resist its damage.

[Sternenwind]

The fireball get cast and flies off and nobody can do anything against it?
The fireball, if not blocked by something physical, hit its target location and goes off and nobody can do anything against it?
The fireball does his thing. Everybody affected can dodge and conterspelling is still not helping?
Everypony that did not get enough hits on his dodge roll gets fireball damage. And now can use counterspelling for the damage resitance test?

[Shaidar]

Dodging a Fireball is mostly guess work. SR4 lacks the interrupt mechanism which exists in SR5.

The fireball get cast and flies off and nobody can do anything against it?
The fireball, if not blocked by something physical, hit its target location and goes off and nobody can do anything against it?
The fireball does his thing. Everybody affected can dodge and conterspelling is still not helping?
Everyone that did not get enough hits on his dodge roll gets fireball damage. And now can use counterspelling for the damage resistance test?

Yes on all counts.

[Sternenwind]

So

SR4A p.185 Spell Defense:
“… When a protected character is targeted with a spell, she rolls Counterspelling dice in addition to the appropriate attribute (Body or Willpower) for the resistance test. Hits generated on this test reduce the net hits of the spells cast as with any opposed test. …”

and

SR4A p.204 indirect Combat Spells:
“… If the spell reaches the chosen target and it fails to doge with Reaction (+Counterspelling. If available). The target then resists damage with Boldy + half Impact armor. …”

can be ignored?
Any references so i can be on the save side?

[Shaidar]

So

SR4A p.185 Spell Defense:
“… When a protected character is targeted with a spell, she rolls Counterspelling dice in addition to the appropriate attribute (Body or Willpower) for the resistance test. Hits generated on this test reduce the net hits of the spells cast as with any opposed test. …”

and

SR4A p.204 indirect Combat Spells:
“… If the spell reaches the chosen target and it fails to dodge with Reaction (+Counterspelling. If available). The target then resists damage with Boldy + half Impact armor. …”

can be ignored?
Any references so i can be on the save side?

Emphasis Mine
Situational Emphasis

Here is your cognitive disconnect. When protected character is NOT the chosen target there is no Dodge test as you aren't the target of the Fireball. So you skip straight to ...

“The target then resists damage with Boldy + half Impact armor & Counterspelling dice in addition to the appropriate attribute (Body or Willpower) for the resistance test.

So Spell Defense still plays a part just not the SAME part as usual because the character isn't the target because a Mage is playing things smart.