1. "...Diseases in Guyana?...Think big like a tiger, big like a giraffe, big like an elephant..." Okay, not too tough I guess. He was referring to lymphatic filariasis, from the nematode Wuchereria bancrofti seen in the adjacent picture. Colloquially this is often called elephantiasis - as the parasites (transmitted via mosquito) destroy lymphatic drainage causing lymphedema which can sometimes be quite profound.
2. "...No wrong answers here...there are only right answers with this arthritis...". Yep, he is referring to Reactive Arthritis, formerly known as Reiter's Syndrome (get it??? '...only right answers...' and Reiter's?) . This is a seronegative spondyloarthropathy (along with Psoriasis, Ankylosing Spondylitis, and Inflammatory Bowel Disease). It can follow infection with Chlamydia trachomatis, Yersinia, Salmonella, Shigella and Campylobacter, and is associated with the HLA-B27 haplotype. It is manifested by oligoarthritis, enthesitis, uveitis, urethritis and sometimes keratoderma blennorrhagica (hyperkeratotic skin lesions on soles and palms)....hence the mnemonic "can't see, can't pee, can't climb a tree".
3. "...It's a steal for you...how your kidneys are damaged in diabetes..." referring to Kimmelstiel-Wilson lesions commonly seen in diabetic nephropathy.
4. "...Does she have hyperthyroidism? Don't lag behind me here...." referring to the lid lag seen in Graves' disease. Other extra-thyroid manifestations include lid retraction, pretibial myxedema, and acropatchy. Here is a recent review on Graves' Disease.
(massive lymphededma in filariasis)
(keratoderma blennorrhagicum in Reactive Arthritis)