My LCD I2C blinks like (it's losing voltage) when the buzzer it's activated. the buzzer does a beep beep sound and my LCD blinks at the same time. it also makes the LCD lose contrast over time and i have to regulate again until it's a max power, once it hapen, i need to dissconect and leave it 5 minutes like "cooling down".
I was thinking maybe the battery, i'ts new but can be faulty.
That simply doesn't make any sense at all. Once you connect any pin to ground, no amount of pulling up is going to shift the pin. It is at ground.
You have no battery on that layout diagram (it is not a schematic), so where is it?
What sort of battery do you have?
Not faulty as such but you could be drawing too much current out of it and it has now nearly empty. Your symptoms match a discharged batteries slowly recovering over time.
What do you see when you measure the voltage from the battery when you are running your code?
Likely overloading the battery, it's output will sag as you're experiencing, and recover(somewhat) when load is removed. Get a decent wall-wart - make sure it's regulated, not a piece of junk. Rating should be between 7 and 10 V, at least 1-2 amperes, because your next project will likely want even more current than this one, may as well be prepared.
Then get a bigger battery, because a smoke alarm battery is just not worth the pain. Look under the hood of your car.
FWIW, I find it useful to use a wall supply for all development, regardless of whether my target is wall-free or not. Reduces the number of error sources. When I finally change to a battery, I can focus on whether that contributes a problem or not, knowing the project works fine on a power supply. But hey, it's up to you.