What was Vader a lord of?
He's a dark lord of the sith. Yes, the empire is secular, but ultimately, the Emperor is a commited sith, and can pretty much decree anything he wants. So he gives Vader the official title. As for his official role, the emperor put Vader there in as his personal representative, and gave him whatever military resources he needed to recover the Death Star plans and later crush the rebellion. Thats all the authority he needs.
How could Tarkin have destroyed Alderaan?
He was Grand Moff, but he was also a military officer, commanding officer of the Death Star, tasked with destroying the rebellion. It was in this capacity that he had the authority to do most anything he wanted to. Also, Tarkin could safely tell Darth Vader off. To be able to do that, one had to be pretty close to the Emperor. So its doubtful that the regional govenor over Alderaan is going to complain much.
What was the point of Echo Base?
The Rebellion probably has too many space fighters and other equiptment to carry on their spacecraft and to store it all in outer space, so they need a base of some sort to operate out of. They can't simply stay in deep space. They need a land base as well. So I'm guessing its basically a giant gas station/repair station/storage facility. Plus, the higher ups in the rebel alliance love riding around on tauntans.
Why didn't the Imperial garrison reinforce the bunker on Endor?
I don't see the problem here. The empire had plenty of Stormtroopers there to handle the situation until the ewoks unexpectedly got involved. They didn't bring out the AT-ATs because they are too big and would end up doing more damage to their own side than the rebels, and it was probably impossible to get them to manuver in the dense forest. So that left only ground troops and the light AT-STs. The troops came in and were slaughtered by ewoks.