Marfan Syndrome: This genetic disorder is characterized by tall stature, joint hypermobility (which could explain the back pain that cracks easily), and other systemic features. The bright red toes could be indicative of poor peripheral circulation, which can be seen in Marfan syndrome due to aortic root dilatation leading to decreased peripheral pulses. Tachycardia might also be related to mitral valve prolapse, a common feature in Marfan syndrome.

Ehlers-Danlos Syndrome: Similar to Marfan syndrome, Ehlers-Danlos syndrome is a group of disorders that affect connective tissues supporting the skin, bones, blood vessels, and many other organs and tissues. Its features include extremely flexible joints, skin that stretches much more than usual, and tissue fragility. The back pain and joint pain could be attributed to the hypermobility type of Ehlers-Danlos syndrome.
Ankylosing Spondylitis: Although less likely given the tall stature and specific combination of symptoms, ankylosing spondylitis is a form of arthritis that primarily affects the spine, although other joints can become involved. It causes inflammation of the spinal joints (vertebrae) that can lead to severe, chronic pain and discomfort. The back pain that cracks easily might be related to the inflammatory process and the resulting stiffness.
Hypermobility Syndrome: This condition is characterized by joints that move beyond the normal range, which can lead to joint pain and instability. The easy cracking of the back could be a manifestation of this syndrome.

Osteogenesis Imperfecta: A genetic disorder characterized by bones that break easily, often with little or no apparent cause. While the primary symptom is fragile bones, joint pain and hypermobility can also be features. The back pain could be indicative of vertebral fractures.
Aortic Dissection: Although rare in a 16-year-old, an aortic dissection (a tear in the aorta's inner layer) could present with severe back pain and might be associated with Marfan syndrome or other connective tissue disorders. The tachycardia and bright red toes could be signs of a significant cardiovascular event.
Infectious Endocarditis: Given the tachycardia, if there's a history of heart murmurs or other cardiac abnormalities, infectious endocarditis (an infection of the heart's inner lining or valves) should be considered, especially in the context of a possible underlying condition like Marfan syndrome.

Stickler Syndrome: A genetic disorder that affects the connective tissue and is characterized by distinctive facial features, eye abnormalities, hearing loss, and joint problems. While it shares some features with the presented case, such as joint issues, it is less likely due to the absence of mentioned ocular or auditory symptoms.
Loeys-Dietz Syndrome: A rare genetic disorder that affects the connective tissue in the body, leading to problems in the blood vessels, the heart, the bones, and the joints. It shares some features with Marfan syndrome but is distinguished by unique facial features and a higher risk of vascular rupture.