CHIEF answered the first part already. Feel free to call people names if it makes you feel better.
The Alamo had more artillery than the Santa Anna army, including the biggest cannon in Texas in the southwest corner facing San Antonio de Bejar. The Texans had captured the artillery from Santa Anna's bro-in-law just 2 months earlier. It was the Mexican Army who wanted to fortify the old mission. San Antonio de Bejar was on the frontier of the Texas, and Bowie & Travis (both sent to destroy the Alamo) saw it as an outpost to fight off the Mexican Army. They both saw it as a post to repel the Mexican Army and preserve Texas. Otherwise, Santa Anna's army could sweep the colonies and basically burn Texas to the ground.
Houston wanted it destroyed all right, but was then ordered to relieve the Alamo from the convention. Houston still didn't believe their was a Mexican solider inside Texas' Mexican state lines for miles and simply dismissed Travis' letters as poitical "party purposes". He didn't ride out until it was too late for the Texans in the Alamo. He got as close as Gonzales when he found Mrs enson and heard about the fall of the Alamo three days later.
CHIEF was wrong about one thing - the Alamo cost Santa Anna more than 13 days. He was an impatient man, who could not imagine a victory without bloodshed. His commanding officers did not want to storm the mission. They simply wanted to wait until the heavy artillery arrived and then they could bring down the walls. Tarvis & his men would either be annilated or surrender. Santa Anna didn't want either - he wanted to kill the Texan spirit in one battle. He would have preferred Houston come to the Alamo and end it with that one battle. That is why Travis' letters sent by courier were able to get thru the surrounding Mexican army continusouly.
Once Santa Anna realized Houston wasn't coming, he was then concerned about winning the war against the 'rebels' with speed. That's what motivated him to move his army from Mexico City to San Antonio de Bejar in less than 30 days - in the middle of the winter, a winter that included a snow storm. That is partly why the Texans ran into the Alamo in the first place - they never expected Santa Anna to arrive so quickly. Of course, that left his army spread across south Texas and northern Mexico.
You might think the battle was "pointless", but Santa Anna would disagree. Even tho he called it "a small affair", he wanted the rest of the 'rebels in Texas' to know what happened to the men of the Alamo. The women, children, and slave (yea...Texans were also fighting to keep their slaves) were sent out to intimidate the rest of Texas.
But probably more important than anything else - the victory proved to be the ultimate defeat for the Mexican Army. Santa Anna, wanting to do everything so quickly (versus the patient Houston), would rather have his men die from their wounds suffered in the battle of the Alamo than to carry enough medical supplies to heal them following the battle. They disarmed the Alamo, and soon began leaving all heavy artillery in order to pursue Houston's army as quickly as possible. Santa Anna then went even further by splitting his own army in hopes of outflanking Houston.
It proved to be his downfall as the army defeated at San Jacinto over a month later was small versus the army he commanded at the Alamo. Nonetheless, Houston's army was smaller than Santa Anna's. But you seem to forget that the Texan army had gathered in anger & numbers by that time. Something as a direct result of the battle of the Alamo - the battle you call 'pointless'.
Oh, and the battle lasted more than 20 minutes. More like an hour. Santa Anna's hopes were to have his men up & over the walls as the Texans slept. That is why he stopped the bombardment & music the night before. The Texans awoke and repelled the Mexican army twice. Crockett and his men defended the wooden fence and forced the south attack down the wall. The northern attacks (north, east, west) all culminated at the north wall, which was a result of the Texans repelling the initial attack plans. Eventually, the Mexican rifleman began picking off the defenders as the looked over the wall to fight off the Mexican soliders at the base of the northern wall. The Mexican army then won by sheer numbers. The Alamo chapel itself was probably the last part of the fighting. The Mexican army turned around the cannons on the walls and blasted the Texans in the barracks and Alamo. Crockett was probably then captured and executed.
Enough facts for you?
FEEL FREE TO RESEARCH ANY OF MY ABOVE CLAIMS IF YOU DON'T BELIEVE ME.
Or do you need me to insult you like a school boy for you to understand, PEE WEE? Take your own advise and research a topic before posting.