If you are only practicing once a week that isn't giving your voice enough time to develop and become stronger. If you're able try to add more on like do 3 days a week to start and see how that does. Are you doing any scales or just the isolation method? Doing scales might help since some of the can trick your voice into going higher where you don't have to think about what you're doing.

When I barely get to A5, my throat feels real coarse and it breaks down to G#5 immediately and I almost cry in despair, it's sooo frustrating!!!

Here is your problem. 1st i agree with Melanie , you dont practice enough. You need to work the voice more and remember that progress is made when you are staying positive , not when you are frustrated. You are like me , you want it immediately. It doesnt go that way. And what's with that 'head voice' thing? Its full voice if it is supported the right way and placed into the soft palate. Forget that head voice stuff. It only limits you. Start with the sirens and make sure you strenghten all notes ONE BY ONE. Focus on the resonance. As you do the siren , start big , end big. Resonance is the key. On the high notes your voice will 'ring'. Take your time and practice at least 5 days a week.

Well girls, thank you both for your advice! I did it, I increased my practice time to day on/day off, which makes it 3.5 days a week lol. Finally, on Mar 11th I WAS ABLE TO REACH CONSISTENTLY B5 FLAT, 5 TIMES! I did it doing chromatic scales, from C5 attempting to reach B5. I was stuck on the ooo ooo ooo's, so I started to do more no no no's instead and, together with the increased practice and some wonderful face, chin and neck exercises I just started doing every day to strengthen the muscles around the neck, I finally overcame the obstacle!
Now, should I keep doing the same and expect to [finally] reach a C6 pretty soon? Or could there be anything even better than doing chromatic no no no's to increase the range?

What you are describing is pulling chest. You need to mix in some head resonances into your middle register before reaching your head register and extend your range. You might loose a bit of volume in the beginning but as you learn new muscle memory, by doing this correctly, your volume will increase and your range will be more consistent. Let me know if you'd like some guidance in the form a a lesson. My info is here:

http://www.valeriebastien.com/VY4singers-home.html

Val

No I'm not pulling chest, Val. I'm an alto, my voice breaks on A4. My head voice is around C5 to A5, where it breaks again. My super-head voice is the register I'm unable to access as of yet, although as I mentioned I was able [finally!] to reach Bb5 several times, the other day, doing No No No's. I wish I knew SPECIFIC TECHNIQUES to be able to access the super-head voice register, since tongue trills --my favorite warm up exercise-- aren't achieving it so far, along with the No's.

Anything that feels like "yelling" is not proper head voice or full voice. I can pull chest on a B5 (and much higher) and it's still pulling chest voice. However, when I do that my throat strains because the larynx is tilting in the opposite direction that it should to find the space it needs to extend the vocal cords. Just saying ;)