Hi there,
I am an American who held residency status in Morocco for two years. My employer paid the CNSS (public insurance) fee monthly, for which I was reimbursed 70% of all medical fees (e.g., medication, appointments, blood tests) after submitting the required paperwork to the CNSS office. I was initially worried as I have a few chronic health conditions for which I take medications daily, some in high doses. I am happy to answer your questions as I know the anxiety than can arise from not knowing what to expect 
 
Have you ever had difficulties finding familiar or useful medicines for your health in your host country?
The ultimate answer is no, there were no difficulties. The only issue I came across was that Morocco does not carry brand medications, specifically for epilepsy (I am not sure about others). Consequently, I switched to generic. This did not pose any problems as it is equally effective, however, it did affect how I took my doses. There were no difficulties with any of my other medications, including birth control.
Have you ever been faced with a shortage of medicines in Morocco?
No. My local doctor supplied me with prescriptions for three months' worth of medication, and the pharmacist always had it ready for pickup either by the next day or within the week. I ordered contacts from an optician once, which took a couple weeks as there is a longer delivery process, but they conveniently delivered them to me directly. 
Would you have said that in Morocco drugs are more or less expensive than in your home country? Do you find them more or less effective or of similar quality?
As an American, the medication I purchased in Morocco is less expensive to an extreme degree. Notably, if you are covered by CNSS, you must pay the full amount upfront for any medical service, and will then be reimbursed after submitting the paperwork (includes receipts, doctor signatures, etc.). For reference, WITH insurance in the U.S., I paid roughly $630 for three months of medication whereas in Morocco paying upfront (PRIOR to reimbursement of 70%), I paid about $700. The quality of the medication is the same that you would find elsewhere. I am currently living in England and the medication I receive here is the same I received in Morocco.
What is the place of alternative medicines in your host country? Have you ever used them?
(I do not have any experience with this)
I hope this helps!