1. When I block with a character with STR 3 against a character wth STR 4, does my character die then? 

2. If an opponent attack with a character  STR 3, can I then block with 2 character against his?

Asked the Moderator to move  this to the Living Card Game Forums

iKontext said:

What do you mean by "block"?

If you mean "choosing a character/ House Card" with strength 3 versus a strength 4, then no, you dont NECESSARILY die, just because he has a higher combat strength card.

I suggest you read again the rulebook from page 17-20 under the combat rules, but if you don't feel like it, here it is:

You win a combat depending on combat strength of your units + defense order token bonus (if you are defending) OR march order token bonus/penalty (if you are attacking) + supporting units (yours or another player's, if he agrees to support you) + combat strength of your house card and effect of its abilities (if there are any - usually a small text) + use of the "Tides of Battle" cards (if any) + use of Valyrian Steel Blade (if any) …

In case of a tie, player highest on the Fiefdom track wins the battle

After taking in account all of the above, the winner can be decided. So, back to your example, both scenarios could be correct or wrong. What decides is the other factors mentionned above…

PS: By saying "blocking", you are probably hinting that you choose a House Card as a response to the other player? I must say, that both of you MUST choose cards and reveal them SIMULTANEOUSLY. 

Hope this clears your confusion…