I have a mole on my back which keeps growing and a non-mole mark type thing, which hasn't changed but still worries me. (photos)

Any changing or irritating mole should be assessed in person by a dermatologist who will be able to determine whether such mole is benign or requires a biopsy. I suggest that you see a cosmetic or surgical dermatologist who can then provide you with options for removal without leaving a significant scar. 

Thank you for your question. Lesions that look like moles can actually be other types of growths that we get as we age or could be malignant (cancerous). In my opinion, any new or changing lesions should be evaluated by a dermatologist, who uses an instrument called a dermatoscope to evaluate the lesion under higher magnification. If there are any abnormalities, then a biopsy should be performed for further evaluation. So I highly recommend you consult with a board certified dermatologist to have your growths evaluated and to discuss treatment options that best suit your needs. Take care and good luck.