My gums bleed. And part of my lower gum is away from my teeth. What home remedies are there for this situation?

Periodontal Disease. Bleeding gums and retraction of the gums away from the teeth are signs of periodontal disease. Apart from brusing with a soft brush, gently flossing and using saline rinses or mouthwash and perhaps some vitamin c, you need to see your dentist or a periodontal specialist and get seen. You may need a prescription mouth wash, antibiotics, special cleaning and perhaps gingival surgery. Don't delay!
Limited options. If you have this gum problem nothing will make it go away without being treated by a dentist. Warm salt water rinses and improved home care wll help. It's the same as if you had a splinter in your finger that was infected. Nothing you put on the finger would cure the infection without taking the splinter out. In the case of your gums, you need to get the build-up off your teeth first.
Bleeding gums. You may have gingivitis or/and periodontal disease. Plaque is a sticky bio film that can be removed with a toothbrush, calculus is a harder and attaches itself to the tooth and root surface and needs to be removed professionally by a hygienist or dentist. See you dentist for an evaluation.