1) Right before the starting player's turn. There were some other clarifications in this thread (look for the posts by SevenSpirits, one of the game designer):
http://forums.shadowruntabletop.com/index.php?topic=17975.0.
2) Yes to your two questions.
3) Indeed, the third scene of the Crossfire mission is tough : I often get out of there alive with only 1 per players. This is a challenging game, some players talk about a 25-50% rate of having a succesfull mission. If Crossfire mission is too hard for now, you can always use the Ambulators mission to get some play experiences, Karma and upgrades : it is basically Crossfire minus the third round. And yes, some "normal" obstacles are really annoying.
Some strategies might help you, so you can look at this forum or BGG for some videos and threads offering tips. You can also ask questions (as you'd just did). Catalyst recently opened a FAQ page with some videos to help players (I did not see the vid yet) and files, including the Ambulators mission I've just mentionned :
http://www.shadowruntabletop.com/shadowrun-crossfire-game/.
In the beginning, I found that game really tough and almost impossible. Sometimes it feels like the cards are drawed in a perfect order to kill you. But after many sessions, I see the logic and planning one must use in a session and now my games are easier : still really challenging but easier. For example, in Crossfire mission, speed is essential in the first rounds : you want to defeat rather quickly your opponent to avoid taking damages and having a too high Crossfire level.
Table talk is also essential so you can determine as a team the best way to play. It is not permitted in the rulebook, but my group often played with the cards face up when we first bought the game. That way, it is easier for the group to plan the next few turns. This might be a problem if you have an Alpha Player who likes to tell everyone what to play, so your experience may vary.

Edit : Namikaze is quicker than me lol.
