I missed your second question last night 'cos too tired already.
下巴甩毛 is not a good sign. It is possible that your cat got skin disease. It is not hard to cure but requires medical attention. Some of these disease may affect human (e.g. Ring Worm).
For Queen (female cat), it is HIGHLY recommended that you do the surgery. First, the cat will "meow" when she is on heat (叫春) and it is quite annoying. Second, just like any ladies, she will have 月經 ... tho' not each and every 28 days. But you don't want to see blood on your floor / furniture or alike.
It is easier for me to type English here at the office ... sorry.
I would recommend bringing your cat to SPCA's doctor for an inspection. You can always ask him / her what could have caused her pissing on the bed as well. Most of the time, they are very willing to offer help and advice as long as you show them you love your pet very much. The charge is reasonable as well.
For other vet., some are good but many are just there for business. They will ask you to do unnecessary test, etc.
A queen will go on heat once it reaches 6 to 7 months old. It will try to jump up on higher ground and starts meowing (normally from 9pm onward). Do you notice anything abnormal for your kitty?
A queen is capable of having 4 litters per year ... that means she can "call spring" at least 4 times / year. One of my previous cat did that once as she matured earlier than we have expected. Really funny experience.
I think my student won't be able to get you the Scatmat extension. The Westin Hotel he is living in is 5km away from any nearby pet shop I checked on the map. Maybe I try to find you another way. As long as it is within your budget is okay, right?
Ha, your kitty didn't clean herself up? That is strange .... really a "dirty cat" like we Chinese says?