Let's discuss the absolute incompetent faggotry of Theoden "king", shall we

WOW. Didn't remember this as a kid. Thankfully we don't have that kind of language in today's movies.

The siege of Minas Tirith in the book is an actual siege, not a billion orcs standing around in a field. The Witch King, who acts as general in the book, instead of this orc, is busy with the outer wall and gate, and does not have massed infantry to set up a wall of pikes with.
The Haradrim don't have giant elephant monsters, they have cavalry. Theoden engages them after collapsing the orcish flank, and defeats their chieftain. (And honestly even if they did have normal elephants like elsewhere in the book it would have been more reasonable)
The battle sequences in the book imitate the style of Saxon epic poems, so the details are less important than enumerating the deeds of the principals.

The CGI didn;t age well.

But still better than The Hobnob.

No, but the orcs can. The Haradrim can. The Easterlings can. They've already retreated, and would likely regroup before the Rohirrim did, and the oliphants would form a buffer between the regrouped Rohirrim and the siege towers. Theoden couldn't regroup because it would've cut Gondor off from whatever help Aragon was also going to deliver. He hardly could've know it would've been a ghost army mind you, but tactically pushing the charge forward into the oliphants and into the retreating orcs was the better choice all things considered.

That, and there are still orcs inside the city, without reinforcements now, for the Gondorian soldiers this is their best chance at retaking the wall and the main gate but only if the orcs in the city remain without reinforcements.

No it wasn't.

That doesn't automatically make a side lose.

No it wasn't, Theoden only got half of the men he wanted. The rest are still behind, ready to defend their homeland. He also never said that the full amount of the men he wanted was all the men in Rohan.

Limit the estrogen in your food already.

Fun fact: 1914 marked the period where cavalry was at its lowest usefulness in the battlefield (their mobility meant nothing against machine guns and shelling), so the infantry had to do the pursuit job. That's why German's First and Second Armies didn't manage to rout the Franco-British troops after the Battle of the Frontiers, because they had to pursuit them on foot; which allowed the French and British to regroup at the Marne to avoid defeat.
Cavalry would rise in usefulness again when it became motorized cavalry later on.

Also, by all the Witch-King knew, Rohan was not coming to aid Minas Tirith; he had the roads between Rohan and Gondor blocked, and there were no reports of a huge force of rohirim walking past them (they used a secret road goinjg through the pukel-men's forest). There was also the darkness that Sauron used to help defeating the morale from Gondor; one of the main themes of the Battle of Pelenor, I think, is how the good guys seize the enemy' weapons to achieve victory (the darkness helped hiding the Rohirim from Sauron's scouts; the Army of Dead helped Aragorn to take the Umbar fleet).

Fun fact: no one, not even historians actually know what real ancient battles looked like or how they were fought in practice. We don't even know their sword fighting techniques, the art was lost and all we can try to do is study the few remaining manuscripts. Herodotus never described the battles in close detail, his audience was partly made up of soldiers and to them these things were common knowledge.

In the books, they leave a small force to defend their garrisons in Rohan. There is an enemy force they leave behind: the orc army that tried to invade Lothlorien, and that Eomer decides to ignore (or else they wouldn't be able to aid Minas Tirith). The ents got rid of them, however.

Probably because those techniques became more and more obsolete, so nobody cared to keep a record.
Don't get me wrong, it would be cool to know for sure how a greek phalanx or the mounted horse archers from the Mongols really worked. It's a shame that, now that we have the means of preserving knowledge on a massive scale, most of it is utter garbage.

That's another good point, doesn't the movie show Aragorn arriving with the ghost army to fight in the main battle for Minas Tirith? They only actually take the fleet of ships that would have tipped the battle in Sauron's favor in the book. Also a main point in the battle is when Aragorn arrives on the conquered boat with the sweet banner Arwen made for him. It's a pretty important moment in the story for several reasons, wish they would have shown it. It's even pretty cinematic.

"I'm the King" gloating wouldn't have fit the movie-Aragorn's character arc. I really wish the ghost army and corsair ships thing was kept faithful to books but I don't know how it could have been done while not breaking the pacing and keeping it unconvoluted for even the morons in the audience.

Half didn't get mowed down. A Mass cavalry charge didn't do so good, but just like in Total War, they take down the elephants with horse archers. Remember when Eomer commands his men to 'Aim for the heads!' that causes the Mumakil to get all pissy and fuckup their own men.

Daily reminder that Uruk Hai are superior race in the middle earth

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These days you can't have the hero spend a normal human's life time scheming for political takeover and then taking the throne after everyone opposing the idea is conveniently dead or dying and he is the only one with a semblance of an army.

Magic ghosts are the solution to everything.

Against whom, mordor? Who else? Isengaard and Dunland were defeated, and Misty Mountain goblins probably wouldn't even make it to edoras

Yes it is.