Problem solved! YAY!
Landlord came here today to install a doorbell (now i have the Jetson's doorbell LOL) and as soon as he arrived i told him about the heater and the alarms going off.
Immediately he almost panicked. And he could instantly remember several months ago he went to the roof to do something and he almost fell. He grabbed the flue.
At that time he didn't pay any attention as the flue didn't visibly move above the roof, however, the part between the roof and the ceiling fell.
He immediately went to the crawl space under the roof and saw the flue was fallen.
Situation: all the fumes were trapped between the roof and the ceiling, and backflowed through the hatch on the hallway ceiling, right next to the smoke alarm that is also a CO detector.
The alarms are linked so when one goes off, the others go off together (that explains the alarms going off at the same time).
I wouldn't expect a better solution knowing my landlord the way I know. He immediately said "for god's sake, please don't you dare to think about turning the heater on today. If the CO alarm didn't go off you could be dead now. Let's turn the pilot off just in case (well, it was already off). You know what? I won't fix that crap. It's almost 10 years old and I personally don't trust it. We never had any problems with it but i prefer to be on the safer side. I'll schedule with the technician to come ASAP and install a new heater AND replace the flue. I prefer to have everything brand new.
The heater is actually made locally (Williams) and he has a relative that works there, so he can get a new heater for a modest price.
Other thing my landlord did today: The porch had a light fixture that was missing the glass globe. The day i moved in he told me he was going to order and come to replace. I thought he was going to order the globe only. Well, he came today with a brand new (and cute) light fixture. And it's visible it's not the El Cheapo brand because that thing is heavy and visibly well designed and made. It also has some fancy features like a sunlight sensor, a motion sensor and it's Wi-Fi enabled.
he also helped me installing the two first blindings (he will replace 2 per month until all of them are replaced) and even touched up the paint to cover the area where the old blindings brackets were screwed.
When we were there, i asked him if he could indicate a window washer to clean the windows, he didn't know any, but he said "you know what? those windows are so old and ugly. Would you mind the mess if i replace the windows? Not right now, but one or two per month on the next months.
I chose this property alone and i decided on it because i was tired of looking for properties and not finding any that would be affordable. What made me pick this one was the huge laundry room downstairs and the brand new bathroom.
Right after I moved, I discovered the property is in one of the worst neighborhoods in los angeles. Now i literally live in the middle of the "hood", the famous zip code 90044. (AKA gheto, skid row, etc).
I was terrified when I discovered that, but my landlord is so cool that I'm starting to change my opinion. My neighbor (the front house) lives here for years and he also told me that we are right in the middle of a series of blocks that have impressively low crime rates because most of the surrounding neighbors own the properties and live in the area for several generations, so drug dealers, gang members, etc are not welcome and don't feel welcomed in this area.
Oh, and next year he will remodel the kitchen, get rid of the old cabinets (horrible by the way) and a silly triangle on the corner that makes the kitchen even smaller. I will have space to have a decent dishwasher YAY.
For now, I'll be more than happy with a 4-service countertop Haier DW that Kevin found in Sacramento and brought to me. He tested it and it works great! i'll pick it up tomorrow night.