The information you provided was insufficient. For example, how long have they lived there? If the lease was for two years and they did not pay rent for the last month, obviously it is not a material breach. Whether it is a material breach depends on the the facts and is a question of degree. The judge has the discretion not to treat this as a material breach and you cannot get restitutional damage. BTW, to get restitutional damage you must return all the money they paid, minus some reasonable value of the renting. I don't think a judge would take the trouble to do this. You may get expectation damage, which is the rent. You may get an eviction.
(2) 把母女俩付的钱分开算是不是在偏袒房客?不仅母女俩都住在那里,而且连她们自己都没有这么认为。
Regardless who paid for the rent, one of them paid the rent for august and they had the right to stay. Does it matter who was the tenant, who was the assignee, who was the subleasee? I think not.
(3) 法官为什么不搭理我反复强调的没有租房合同的问题?
The truth is there is a contract. For one month lease even an oral contract would suffice. The moment you took the $1145, there is contract formed. Even if your jurisdiction specifically needs a written one for statute of frauds purposes, there is still a contract because they paid the rent and took possession. Eveidently there is a contract. Something we call doctrine of partial performance. One way to bypass statute of frauds.
(4) 为什么不让房客有书面的东西说明已搬出。现在我说房客在法庭上说谎,法官可以说他没有听见。
For a fixed term lease, one month, tenant has no obligation to notice. Not sure that is your question though.
(5) 为什么法官在明知房客没有合同,也没有交9月份的房租后,仍没有给我writ of restitution? 即使在我打电话去之后仍然没有给我writ of restitution, 只是叫我重新再来?
Because what the judge said, the original lease was void. You started a new lease, fixed term for one month, with the tenants. This is a different cause of action and you have to file a new claim.
(6) 最重要的是,法官没有给我一个书面的文件可以进出租屋,房客可以告我骚扰,丢失物品等等,我还真有大麻烦了。法官不是在坑我吗?
Fixed term lease ends automatically at expiration date. You have the possession at the end of the lease. Anything left inside becomes yours, at least under common law. You even take posssession and sell those thing under doctrine of distraint if rent was unpaid. Modernly, you may have to go to court to file an eviction claim.