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I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
If your current lease doesn't have an expiration date, then you are legally considered a month-to-month tenant. Your landlord can terminate the lease and ask you to leave at any time, as long as they give you proper notice. That also unfortunately means they're allowed to raise the rent as long as they give you proper notice. The fact that the current lease doesn't have an expiration date doesn't mean that they're never allowed to raise the rent or ask you to leave.
You can choose to refuse to sign a new lease, but if you do, they will increase your rent and you will remain a month-to-month tenant. That also means you'll have the freedom to terminate the lease and leave at any time (as long as you give notice), and they'll have the freedom to increase your rent at any time. Or you can choose to sign a new lease, with only a $10 increase, and they won't be allowed to increase your rent again until that lease ends.
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