In order to make time for writing I must give up working or gaming...
Q: Discard all cards played from hand?
I assumed all cards played from the hand (including reflexes) are put on the discard pile but I can't find this explicitely mentioned anywhere in the rules.
Yes - though some cards (a tiny few and they're powerful) instruct you to Bury them instead
Q: Pay "focus" cost for embedded actions?
Usually, starting an embedded action has a focus cost associated with it. Is this in addition to the cost of the embedded action or instead of it's cost. I.e. Reflex lets you do an action for +2 focus, the action itself is +1 focus. Does this mean +3 focus or +2 focus?
Yes, you pay the Focus cost for every card that is played
Q: Discard/put-on-top weapon cards when action started from embedded action on another card?
I assume all rules of an embedded action or to be followed, but this makes some of the hand cards which start embedded actions very weak. Is this really how it's supposed to work?
Yes, you follow all the instructions on every card. Each Hero Deck contains various clever little 'engines' to offset the problem of discarding/top-decking Weapons every time they are used (and indeed some Weapons, like the Short Swords used by Aseke and Durgen - but not, notice, Elatha! - stay in play after use; in the base Misfall game, Crow and Ardenai have Daggers which stay in play and in HotM there's a Reward item called the Arcane Dagger that stays in play).