Good questions - had these same ones (except for the cats) and didn’t find definitive answers so I’ll tell you what I did to mitigate your/my concerns.
I have a P1S for non-commercial use in my home office a foot from an outside window and four feet from my ears.
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fumes - yes. Have not found air quality testing info online (edit - see below). There are definitely fumes but who knows what they are and how much.
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Noise - yes. I have not found sound level info online. With the door closed, the print head moving back and forth is loud enough to hear and be a nuisance. Everyone will react differently.
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Ventilation - looked at ventilation tents but wasn’t happy with the options so have mitigated with a 4" AC Inifinity grow tent blower from the P1S through the window. Typically during printing I run it ~6/10 setting. Its winter so I’m blowing warm house air to -0c outside but its worth it to me.
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Closed - yes, from a cat entry consideration, no, from an air flow consideration. How smart are your cats? Can they hook a 1x2cm door handle and give it a good tug? The p1s is not a sealed unit. I haven’t seen any literature online for air flow through the frame. Gaps in the door, top, poop shute, etc.
Hope this helps.
edit - toxicity info.