Hello, I am Dr Ola and I would happy to address your concerns about Penny. Unusual urinary symptoms in cats can be secondary to a medical cause or a behavioral issue. Medical issues associated with urinary symptoms in cats can include bacterial infections of the kidney or bladder with or without the addition or urinary stones, or sterile idiopathic interstitial cystitis which is an inflammatory condition of the the bladder wall that can sometimes mimic symptoms of an infection though no infection is present.
First, all medical causes must be ruled out before considering a behavioral cause. You mention that you have seen some spotting starting around 2 weeks ago..the history of spotting with the addition of increased frequency of urination with inappropriate (out of the littler box) can be strongly indicative of a bacterial infection or interstitial cystitis with concern of stone formation. My recommendation is that you is that you make an appointment with your regular DVM and explain these symptoms. The following diagnostics would be what I would I would recommend for Penny- Blood work including a complete blood count (CBC) which will help determine systemic infection, a blood chemistry to evaluate kidney function, electrolyte levels and rule out other metabolic diseases (such as diabetes which predisposes to bladder infection), a complete urinalysis which should include both a urine dipstick and urine sedimentation (to rule out crystal in the urine). Based on your veterinarians physical exam and palpation of Penny's abdomen and bladder (along with urine sediment results) he/she may also recommend the addition of abdominal x-rays to make sure that kidney or bladder stones are not present.
Urinary conditions are becoming more common for indoor cats especially and can sometimes by associated with diet. Based on results of above test, your vet may also recommend a change in diet (to a urinary prescription diet) that can be helpful in the the event of bacterial infection, urinary crystal formation and/or sterile inflammation of the bladder.
Only in the event that medical causes are ruled out can behavioral issues be considered. If you have other cats however, I would consider using an enzymatic urine cleaner (most pet stores have this) to clean up the areas Penny has frequently urinated.. Without enzymatic cleaning, cats will still smell urine and repeatedly urinate in these areas!
I hope this advice was helpful to you. Please let me know if you need clarification on anything or have other questions about this. Also, please do not forget to rate my answer which I hope you found to be "excellent." You may do this by clicking "rate our conversation" below (Your rating is the only means of compensation I receive for answering your question). Again, let me know if I can help you further:)