1) It says you can block one dice, and it's done after the roll, so I was wondering...who chooses which die is blocked? It'd be obvious if the target chose before the attack happened, but that doesn't seem to be the case.

2) If you have two shields of the same color, can they be added together, or can they only block multiple dice? Because if you can choose which one(s) to block, and someone rolls a 1 and a 10 on another dice, you'd want to block the 10.

On a sidenote, usually when I ask questions when starting a new game I'm hoping for one particular answer. But with what I've wondered so far, either way would still be just as fun...I just want to be prepared for tournaments.

Short answer: It doesn't matter.

Long answer:

Shields only block the damage from a particular die, not the attack value -- that die is still used to determine whether or not the attack is successful. Note the combat order from the rules:

Step I is where the results of the attack and defense rolls are compared. This is before the shields take effect in step J.

As an example, say my opponent rolls 2 black dice and comes up with a 2 and a 10, which is enough to beat my modified defense value of 9. His attack is successful, regardless of my single black shield. After the success of the attack has been determined, the 2 and the 10 are equal for purposes of allotting damage. They are each worth 1 click of damage, so it doesn't matter at this point which die I would choose to block.

but what does the number on the shield indicate? it's quantity? or the attack value on the dice with the same color?

The shield blocks any number lower than the printed value of that color. If the shield is a yellow 4, and the 2 die rolled are a yellow 3 and a yellow 5, you could block the 3 with your shield. If the dice were a 4 and a 6, neither would be blocked, as the number has to be lower than the printed shield value.

What about on the base? The 10 is above a blue shield for Lothan, does this mean his shield can block any blue dice role of 10 or less?

the 10 is his defense
the blue shield on his body means take away one blue die
regardless of the number
does not appply to aces however