nope, no cat is crazy to pee anywhere but a box.
A shiney coat means nothing. The 3 cats I had that were dying of aids all looked healthy.
This cat needs a blood test to check for kidney issues and to get checked for cystitus
Cats and cystitis
Inflammation of the bladder (cystitis) is a relatively common problem in the cat. The symptoms include frequent urination, or repeated attempts at urination with passage of only small amounts, plus difficulty and pain on urination, and blood in the urine. Other signs include urination in places other than the litter box (often the bath or shower), or behavioural changes such as depression, aggression or urine spraying.
Cystitis can sometimes result in a blockage of the urethra (the tube connecting the bladder to the outside), particularly in male cats. The bladder then fills, becoming painful, and potentially producing damage to the kidneys. This can be rapidly fatal, within 24 hours. It is vital that any cat that appears unable to urinate is seen urgently by a vet.
What causes it?
The precise cause is unclear, but factors that contribute include stress, a low water intake and the production of urine containing mineral crystals. Unlike in people, cystitis is not usually just an infection, although this occasionally occurs in older cats, especially those with kidney problems. Overweight cats and indoor cats appear to be more prone, possibly because they are less active