for the first question, that depends on what you declare you readied action to be; I brace against Lord Tramplealots, or I brace against the first orc to charge me.
For the second, the character needs only be charging, not targeting you with the charge. This is how a spearmen repelled cavalry so effectively. They getting brace poked by several spearmen, not just the poor guy they tried to run over specifically.
Readying a Weapon against a Charge
You can ready weapons with the brace feature, setting them to receive charges. A readied weapon of this type deals double damage if you score a hit with it against a charging character.
This doesn't actually state that you have to call out who you're "bracing against", but it's not exactly clear that you can "brace against everyone" either. So, I'd say just follow the Readied Action rules for this.
But, let's consider Schiltron formations that were used in William Wallace's time. They had an entire wall of people with long spears who were bracing against the "first horse that charges me", and were highly effective. Tbh, I don't see why you couldn't have the option to specifically brace for Lord Tramplepants or why you couldn't specifically brace for "the first orc" either. I'd say both work fine.
You can be specific if you want to, but simply stating that you ready an action to brace should be fine. The Kobolds hiding in the bushes with their Longspears braced do not care who charges into the bushes first.
If you want to expand the utility of Brace... the Phalanx Soldier Fighter can brace a weapon as an immediate action, and Weapon Trick for Polearms allows you to give up an attack in a full attack to ready to brace a weapon.
When I GM I lean to flexibility on bracing weapons as I rarely see it used. I'd accept I ready an action to brace my polearm if the Gorgon charges or to stab it if comes into reach. May as well give the PC some advantage for carrying a brace weapon (Brace: If you use a readied action to set a brace weapon against a charge, you deal double damage on a successful hit against a charging creature)
I guess if I started to see it being used a lot I might reconsider - but in lots of campaigns with lots of players - I've really only seen new players (initially) excited by the double damage & it never really coming into play.
Think of brace as applying when ever you make a readied attack and the attacker is charging. They don't have to be charging you, they don't have to be even moving through a threaten square (because I can think of a couple edge cases where you have no threaten squares but can still respond to someone being in your attack's reach), you just need to be taking a readied attack and your readied attack has to be happening on someone who is in the middle of a charge you are interrupting.