Ok, here are my conclusions, based on GW & community FAQs and my own thoughts. The topic has not been fully resolved by GW.
1. The GW Mordor FAQ states that the war drum (Mordor Troll) cannot affect the Mumaks Trample move.
2. There is no answer weather or not the Mumak is affected by heroic march. There is no extremely clear sentence which says if a Mumaks move counts as charging or not.
The Fallen Realms source book says when it fails to wound it stops "exactly like a charging model" or in my translation - exactly like any other charging model. To me, this is a direct comparison to every other model in the game except the GBoG. The reason behind the trample rule is to give it a realistic attack comparable to its size. There is no reason to suggest it is different in any other manner, so in my ruling, and what I think is both logical and sporting, the trample counts as charging "exactly like" any other charging model.
Therefore, as it counts as charging, it cannot benefit from Heroic March in order to trample as you cannot charge when affected by a Heroic March or by a drum.
3. The Mumak is listed as a (Mumak, Monster). It therefore is able to access brutal power attacks. The most significant of these is barge, which allows it to charge again, to a maximum of D6".
The GBHL crew have ruled that it is not permitted to trample as part of this move (community FAQ).
The Mordor FAQ states that the Great Beast of Gorgoroth CAN use its own Slam rule as part of this brutal power attack. The intention of this Brutal Power attack was to stop monsters being tied up by 1 warrior and thereby make them more realistic.
I therefore think that we should continue with the intention of GW in making the rule and by allowing the GBoG to use it and say that the Mumak may also use its trample rule as part of the power attack, but remains restricted to D6" in movement.
4. The Fallen Realms source book states that the Mumak is never affected by Heroic Moves called by heroes other than its own commander. It also states that the Mumak Commander's heroic moves affacts the Mumak, even though the base is more than 6" away. This is because the Mumak is treated as his mount (under the crew section). Just to emphasize, this does not make it a Cavalry model, as it is not listed as such, it is just "treated as", to make things simpler.
That GW has made a point about the bases being more than 6" away I think is very important. This indicates that measurement is from base to base. Normally this is not important as everything is virtually horizontal. However it causes an issue with the Mumak which is, can it be affected by a Heroic March of another hero (without trampling). The answer I think is yes, it can, but the caller of the Heroic March must be within 6" of the Mumak Commander (or warrior controlling), base to base. Therefore I don't think it is possible for any other hero to be in range of the Mumak Commander unless they are on a hill or other elevated terrain piece.
In addition, as the Mumak as "treated as" the commanders mount, it would be affected by a Heroic March called by the Mumak Commander (he is basically calling it to himself anyway) and would gain 3" (not 5" as it is not listed as "Cavalry"), therefore being able to move 11", without trampling or charging.
5. Heroic combat, by extension, count as a move but occurs in the fight phase. There is nothing to forbid the Mumak from participating in a Heroic Combat. It starts to get very messy here.
Firstly, the Mumak Commander can call a Heroic Combat and it will affect the Mumak, just like any other call he makes - I am sticking to the same rule for consistency and to make it easier to remember and decide. The Mumak can therefore trample twice and move a total of 16" (8 +
in one turn.
If another hero in base combat with the same model as the Mumak calls a Heroic Combat, it states that "any models from his force engaged in the same fight (except supporting models", may move again. For once this includes the Mumak, as it is not range limited like other heroic actions. Move and trample with the Mumak like normal.
This might seem very powerful, and it is, but having a hero so close to the Mumak, and being able to charge the same model, is very unlikely to occur, and would mean a quick death for the hero on the ground if the Mumak trampled. You could also trap him against the Mumak.
Carrying on from this is an even rarer situation. Say Haldir, Defender of Helms deep (or any other model who may strike blows or deal damage when losing a fight or dying), loses the fight and is killed. If he successfully wounds the Mumak and it fails its test, causing it to stampede, it will stampede as normal at the beginning of the next evil move phase, exactly as specified in the profile. The question becomes, does it continue its heroic combat at all (controlled by good or evil?) or does it lose the ability to. My personal ruling is that it loses the ability to participate in the heroic combat any further (imagine it rearing and screaming in pain while the rest of the fight phase is completed.
NB: I did want to say that it would stampede immediately in favour of the good side, but the profile states at the start of the next move phase, so that's a shame
.
6. Heroic Combat has in brackets (Fight Phase) in the Hobbit mini book. As a hero may only benefit from 1 heroic action per phase, you are permitted to move again and to trample, even if you benefited from a Heroic March earlier that turn. Heroic march, and its restriction on charging is stated as lasting "in the same move phase" - as the move phase is over and it is now the fight phase, there is no restriction.
If you had a hero in the same combat (from the previous example) who called a Heroic Strike while your Mumak Commander called a Heroic Combat, the result is initially unclear.
The Hobbit mini rulebook states that you may only benefit from a single heroic action in each phase. Read as written, the other hero would not be permitted to move as a result of winning the Heroic Combat. However, the GBHL crew have decided that what the rule means is that you may only benefit from one of that type of Heroic action per phase.
This is consistent with YEARS of FAQ's dealing with people trying to abuse the Heroic Action function, particularly by trying to chain together heroic combats and essentially end the game in 1 turn. I give weight to the GBHL crew as they have been in contact with some people from GW in order to sort these things out for their tournament. Elendil may benefit from a free heroic combat because of his wargear, so having the restriction on him makes him virtually useless under the current rules as he can just be beaten with a Heroic Strike, so benefiting from one of that type of action as opposed to one action only makes complete sense.
To summarise, I would say that the hero CAN move as part of the heroic combat, but obviously would not be able to move on again if he joined yet another successful Heroic Combat. Also, as It states that heroic actions must be called at the start of the phase, technically you could NOT call a heroic strike when joining a second combat, as it is no longer the start of a phase - another model in the same fight would be required to do so.
6. Lastly, A Mumak commander cannot Heroic Strike to increase the Mumaks FV. He can only do this is his own base is in contact with an enemy (who may have jumped in the Howdah). He cannot use fate on behalf of the Mumak, though he can make courage checks, as is described in the Fallen Realms source book.
TLDR/Short form summary.
A Mumak counts as charging when it tramples.
A Mumak CANNOT have its trample range increased by Heroic March or a drummer.
A Mumak CAN benefit from a Heroic March IF the caller is within 6" of the Mumak Commander or is the Commander.
A Mumak receives a 3" increase in movement from Heroic March, as it is not Cavalry.
A Mumak CAN trample in the turn it has heroic marched but only if it is as a result of being in a Heroic Combat.
A Mumak CANNOT benefit from a Heroic Move called by any hero other than its commander.
A Mumak CAN use Brutal Power Attacks.
A Mumak CAN trample as part of a Barge Power Attack, but is limited to D6"
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) You can call a heroic march, but with a march you are not allowed to charge, and I think the mumak trampling through the lines is considerd charging. 
