(Psi)SeveredHead
Adventurer
Quick Rapier is a 3rd-level magical weapon type with a daily power. The daily power gives you a free action melee attack against any target after you've successfully hit a target already in the turn. It's from Adventurer's Vault (I just looked it up on Compendium).
Takedown strike is no action, again triggered by hitting someone and just adds damage and a prone.
Backstab just adds damage to any attack. So... yah, they all stack.
It's all legal.
Wow. You've just described why I hate the Character Builder. It's so hard to "throttle sources" (that's something I ranted about once). One of these days, soon, I'm going to post my little rant on the CB, and I'm going to quote you as one of my examples. I don't think anyone playtested all that stuff together. I can picture whoever playtested the Rapier of Quickness might have used it with a thief, or the mercenary background the same, but I'm reasonably sure they weren't all playtested together.
Actually, I have been a WotC playtester before (just once, and did some third party stuff too) and there's no way that stuff was all playtested together.
Hard to do when you have to bring characters to a game either online or before the game starts, like at a game store where you don't know who or even how many people will be playing. In a home game, ok, you might discuss these things before playing, but even then it depends on who you're playing with and how well you know each other.
Seems like you have to try.
I used to assume everyone would play DnD the same way, a view I developed with 18 years RPG experience, and got frustrated when some players decided to build wealth rather than build adventurers (as one example). I was "forced" to explain this before my current Dark Sun campaign. I haven't had such problems since, but it really felt like I suddenly realized these DnD players I'd known for years playing RPGs for years had grown up on other planets.
You really need to talk to them. Even if it's just by IM.