This is an interesting topic. I believe the responses I'd have chosen have already been said, but I'd like to ask a nother question: if you'd be the red player, and the enemy would be the blue and responding in above mentioned ways, what would be your counter-response?

(All flanks below are from blue's perspective)
1. blue responding by striking left flank hard - if blue amasses troops on one flank, try to move own line towards that direction to present a straight line, while at the same time rushing the flank force in. Alternatively, retreat the line backwards to the right, while rotating slightly to keep it facing the direction where blue is.

2. This one is tricky for blue. I'd say strike one flank hard. The best response from red is then to rotate the line struck to face the enemy, then widen it in order to form a good pinning force. Perhaps making a miniature of formation 3. If blue sends one delaying force to the other flank force, there's a tough choice between sending some of the troops to support his outnumbered men or using an entire half of his force to crush the small delaying force before sending his delayed troops into the rear (hopefully) of the enemy before the pinning half of his army is routed. The choice depends on how fast-killing the troops are, i.e. if the outnumbered force can last long enough until the reinforcements arrive.

Another possible response for blue on the split up in two forces is to form a wedge like formation bulging towards the enemy, but it's dangerous as it usually results in surrounding in one way or another. However, if there's supporting cavalry it's a valid option for the infantry line, in fact it's sometimes the best for the infantry to do, as it's the best way of avoiding presenting the rear or flank of a pinned own force to the enemy force. What should red do in response? Well, red can't get supporting cavalry into position very fast, so I'd say red is in most trouble as any attempt to cavalry charge in support will be replied to with a blue cavalry charge to the rear of the red.

3. This formation is very, very strong in infantry to infantry combat. I'd say the best response to it is red's formation in situation 2. If we mix in cavalry, any infantry formation that's as wide as red's formation in situation 3 works for blue, as long as a cavalry charge can hit the middle rear of the enemy line. Without cavalry, using formation 2 is the best. Since formation 3 is usually so effective, the opponent is seldom eager to break it, and may wait longer until doing so in my experience. That's usually enough to hit both flanks of the enemy. The enemy will usually not be able to reform into any good counter-formation quickly enough. If cavalry is involved on both sides, I'd recommend blue to use a thin line all the way, then keep half of the rest of the infantry in reserve behind the line. Then move all cavalry and half the reserve infantry around one of the flanks, using the other half of the reserve infantry to delay an enemy cavalry or other flanking attempt.

What red can and should do is be prepared to leave this formation quickly at the slighest trace of such acts from blue.

4. Flanker deployed in a valley means it's great to use the hitting of the enemy flank with much of the force kept in reserve and it's flank folded backwards. Flanker in valley must rush in order to not arrive too late, and rushing will make him tired.

What should red do? Red should never be in this situation unless the advantage of flanking is huge, i.e. if the flanking troop is a very special type of skirmishing or harassing unit. Red will always be at a disadvantage from this situation unless the unit in the valley can be a tempting trap that makes the enemy send much of their troops down into the valley. Then red attacks outnumbered blue left on the hill, then turns to fight the blue downhill. Against a good opponent, red should never have tried flanking with the valley unless using it as some type of bait.

5. Enemy flanker deployed on hill. This will most likely turn out to become a race for the high ground. As red already has more troops in place on the hill, he has a slight advantage. Blue will should try to get the high ground or retreat so far away from the high ground that red can't fire missiles or anything from it, and must leave it in order to threaten blue. Red's response to the first is to fight the climbing blue with red formation in situation 3 or similar (the height advantage is added the the powerfulness of that formation). If blue tries to use the counter for formation 3 here, red will recive assistance from the other red troops climbing the hill soon, so as long as they try to present a front and no flank to the climbing enemy they should be fine. If artillery is involved in the fight, then red should definitely have deployed it all on the hill, both because of the range advantage, and because of the temptation it means to the enemy to rush the hill rather than choose the more sensible option of retreating out of missile range from the hill.