Welcome to the shadows, chummer.
MATRIX
1) Is there any way to detect if someone is trying to hack your commlink? I would imagine that an alert might broadcast something to your PAN, but would you know as the hacking process occurs?
There are two basic ways of hacking: On the Fly and Probing your Target. Both attempts may be detected, but the rules differ. See SR4A pg. 235.
2) If a hacker succeeds in hacking herself an account on a node without triggering an alert, how can this intruder get detected? Would IC or an Agent be able to detect that this Icon has a hacked subscription? What if it is a security or an admin account?
If you manage to hack yourself an account, you're not an intruder but a legitimate user as far as the system is concerned. It won't have any reasons to react to you as long as you don't do anything that is not within the account's rights, e.g. shutting down security cameras when you've got a basic user account. If active patrol IC is present in the node, the GM may have it analyze the hacker's actions as he sees fit.
However, this is mainly the reason why the corps still pay security spiders. A human can spot odd things going on where software does not. If you've got an admin account for Aztechnology headquarters you may use it to shut all security features down, but someone in the office will notice and come after you.
COMBAT
1) Is it possible to shoot with a simple action and then duck fully behind cover with your second simple action so that you could incur the blind fire + intuition (rather than agility) penalties on your opponents?
Yes, it is, and you get the bonus for Good Cover (+4), too. That's where the rules for destroying barriers, grenades and indirect combat spells come into play. Or you go for the tactical approach and try to get into a better position.
2) How do you rule a critical glitch in scenarios with someone who normally has a high, but radically reduced dice pool? I understand that this is a creative GM question, thus I am asking for experience. Take for example, someone who normally rolls 16 dice to shoot a pistol. They are obviously skilled. Through modifiers, they are now rolling 5 dice and critically glitch. It's hard to imagine someone who is such an ace accidentally shooting themselves in the foot. How have you ruled in these situations?
Well, drek happens omae. The result of the glitch does not have to be related to the character's actions but may also be caused by plain bad luck. The weapon could jam and become unusable, explosive rounds detonate in the barrel, a software bug in the smartlink might cause it to spam false positives all over your field of vision, the recoil makes you slip on wet ground and you sprain our ankle...
Also, keep in mind that glitches can be downgraded with edge.