Yes !!! You can do something about all of this
First thing is to call code enforcements right away and let them know about your heating issues. That is a instant violation especially with a baby in the house.
They will tell you what to do there after
We have the same exact problems.
We moved into our house Oct. 1st and the first thing to give us a problem was the A.C. which took them a month to fix. I was pregnant at the time with 3 children in the home.
Then in the beginning of Nov our plumbing went.
It was horrible.
I called code enforcements because we too did not have any heat
they showed up the next morning
Same problem that you are having, we have. With the calls and how they are never answered or returned.
We are dealing with a management company due to an absentee owner.
This guy is horrible
We finally had to go to court about it because we had no plumbing for 2 months and I refused to pay rent
By law if you give them 10 days notice prior to your rent being due, you can withhold the rent. But send the intent via certified mail.
Need more info
Please email me
C.