That very much depends on the cat and the type of coat they have. Some coat types have a tendency to get very compacted and/or matted if they aren't bathed regularly to loosen the shed hair. Some cats are unable to properly self-groom and need regular bathing. Sometimes a cat gets into something really nasty and letting them self-groom could make them very sick.
IamSparticles
Anya does this to me at bedtime. She waits for me to get in bed, then jumps up on the bed, walks up the length of my body, sits on my chest, gets right in my face and demands all the scritches. If she feels like we are staying up too late, she gets upset and starts meowing loudly to let me know it's time for the evening scritches.
Your filing system is impeccable.
I've never understood why people do that. There are so many shelters that will happily take a surrendered kitten (or adult cat), no questions asked.
Thanks for taking her in. She looks like she's very loved.
That's normal, though. Interior doors nearly always open into a room.
See also: ribbons
One of our cats has a really unhealthy obsession with ribbon. The sort used in gift-wrapping or for party balloons. If anyone happens to leave a piece of ribbon lying around she will absolutely find it and try to eat it. More than once this has resulted in massive vomiting and/or diarrhea.
"It's got force feline"
I still flush the Naturally Fresh. It's biodegradable and shouldn't be a problem unless you're on a septic system or something.
Don't know if it's helpful or even compatible with your device, but about 8 months ago I switched our (non-automated) litter boxes over to using a new litter, "Naturally Fresh". It's made out of crushed walnut shells, and they market it as having natural odor-control properties. It's also significantly cheaper than the "World's Best" cat litter we were using previously. For my part, I attest that the marketing is not just hype. We keep a litter box in our downstairs powder room which guests typically use. Several people who have visited with us since the change have commented on how little odor there is and wanted to know what litter we're using (mostly other cat owners). Alternatively, you can buy odor-control litter additives at the pet store. I've used one made out of (I think?) wheat bran that works pretty well.
I've paid the local cat shelter adoption fees, but I don't think that counts. It helps them stay in operation, and covers things like spaying/neutering.

Allergies can change over time, and also can become more severe with repeated exposure. You can consult with an allergy specialist to get tested and some advice, but there are a few suggestions here already that should help alleviate symptoms. The biggest one is probably to change and wash your sheets frequently (like at least weekly). And use a wash cycle with hot water.
There are lots of options for allergy medication, too. I have really bad pollen allergies, but I've been using Nasacort daily for many years now, and they hardly bother me at all except a little at peak season.
If you think you can manage it, regularly bathing your cat will reduce the amount of dander in his coat. At the very least, try to brush him at least a few times a week with a de-shedding brush, in a different room. I find the Furminator brand brushes work really well on most cat coats.