I suggest that you visit a dermatologist and have them check out the mole on your nose. They can tell whether the mole is a benign or malignant one. However, based on the diagnosis, surgical removal or any other alternative mode of treatment may be recommended by a dermatologist. I suggest consulting a dermatologist near you for further advice. The treatment cost is determined by the recommendations and location of a particular clinic.

Your skin might be affected by acanthosis nigricans which is identified by dark patches, even on the throat and joints. Being overweight and having high blood pressure are risk factors for this. The treatment is to lose weight and control the BP, as a result, the patches can be healed. Follow a healthy diet, exercise regularly, and be consistent with your prescribed medications to control your blood pressure.

A tanned upper lip and pink lower lip might seem perplexing, but it’s pretty common. The simplest explanation would be sun exposure since our upper lips are generally more affected by the sun than our lower ones are. To tan less and protect your lips, you should always apply sunscreen before going out into the sun; if you want extra protection, use SPF lip balm as well. Eventually, the colors will even themselves out.

Worry does not leave marks on your skin. Howe­ver, it may cause restle­ssness. Restless pe­ople sometimes scratch or bump into obje­cts. This can result in bruises forming. Fee­ling tense weake­ns your body's defenses. A we­akened immune syste­m makes bruising more likely. To pre­vent stress-relate­d bruising, you should find ways to relax. Try calming activities, exe­rcising regularly, and eating nutritious foods.

It might be that your underarms have become darker due to some other reason. So, it is best to consult an experienced dermatologist. The dermatologist may examine your condition to know the exact cause of it and determine a suitable treatment accordingly. 

It is not unusual for the untreated cut marks to turn into scars. Maybe the diluted glycerine solution will not be sufficient to help. You can consider adding some aloe vera gel to speed up the healing. Ensure the cut area is cleansed and well moisturized to let nature do the rest of the healing.