The analyses of a text #1

The protagonist, Philip moved in with his uncle Mr. Carey, the Vicar of Blackstable after his mother's death.
He goes to the medical school St. Luke's in London.
He became an out-patients' clerk.
Here "he" refers to the physician Dr. Tyrell.
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He leaned back in his chair, chatting with the H.P. while the porter herded along the old patients. They came in, strings of anaemic girls, with large fringes and pallid lips, who could not digest their bad, insufficient food; old ladies, fat and thin, aged prematurely by frequent confinements, with winter coughs; women with this, that, and the other, the matter with them.
[Of Human Bondage by Somerset Maugham]
1. I'd like to know if "this" refers to "winter coughs."
2. I'd like to know if "that" refers to "anemia."
3. I think "the matter with them" refers to "this, that, and the other."
If so, I was wondering why if it is "the matter," not "matters."
Thank you in advance for your help.