If my opponent makes me discard a card and I choose a creature card with the Bloodrush ability, can I pay the cost during the forced discard in order to activate the ability?
No you cannot. The ability you are looking for is called madness. Here are the cards that have madness: http://gatherer.wizards.com/Pages/Search/Default.aspx?action=advanced&text=+[madness]
No, for two reasons. First, you don't have priority (and thus the ability to activate bloodrush) while your opponent's discard spell is resolving.
The only time you could activate bloodrush is either in response to your opponent's spell or after it is done resolving (when you have priority again). Note that discarding the card is part of the cost of activating bloodrush. If you activate bloodrush in response to the spell you have to discard your card before your opponent's spell resolves, meaning you still have to discard another card when their spell resolves. If you do it after their spell resolves, you still have to have the bloodrush card in your hand (because you discarded something else) in order to pay the bloodrush cost.
Also, as @John said, the madness ability does what you are describing, not bloodrush.
No you cannot. If you activate the Bloodrush ability of a card you have to discard that card as part of paying for the ability, thus it is not a valid card to be chosen for the discard effect your opponent is using on you.
This is how it would end up working:
- Your opponent targets you with Funeral Charm choosing the discard mode.
- Before the Funeral Charm resolves you have a chance to cast spells or activate abilities like Bloodrush. If you do the spell or ability will go on the stack above the Funeral Charm and resolve first.
- It doesn't matter if you activate a Bloodrush ability, the Funeral Charm is still on the stack and will resolve after the Bloodrush ability if you activated it. While it is resolving all you can do is choose a card to discard, you cannot activate any abilities or cast any spells.