As
nznity mentioned Fentanyl is used in the hospital setting quite often. As he mentioned surgery is one area were the use of Fentanyl is quite common. In terms of people directly consuming it on purpose it's not uncommon by any means. When they were more commonly available on the street Fentanyl Transdermal Systems were at least in my area quite highly sought after. Users would break down the patch & IV the Fentanyl. People also would use the patch via bucall administration or in some cases just wear it. I have experience with all three methods. Though not all that much personal experience as I always found Fentanyl to be one of the least recreational opioids.
I've worn the patches for pain relief &/or maintenance at times as well. That would be my preferred method of usage. Bucall was a decent method of admin when my tolerance was low enough. However; I had friends who found Fentanyl to be the best thing since sliced bread & would seek out said patches. As usual the appropriate disclaimer is required. I do not in anyway recommend the usage of Fentanyl Transdermal Systems in the manner I have described. Messing with F patches is a good way to die. I won't go into the number of times I've had to deal with people oding on Fent.

Suffice to say that way before Fentanyl analogues became a thing in 'Dope' I'd had to institute a no shooting Fentanyl at my spots rule for multiple people. One friend in particular would fall out every fucking time. Bring his ass back, repeat. Sadly enough that friend is no longer with us. RIP.
Back on topic yes it is used intentionally for many reasons. As I mentioned I personally am not a big fan of using it outside of it's intended purposes. One of the other concerns with the patches is the range of Fentanyl contained. For example the 100mcg/hr patches varied IIRC by as much as 4+mg. I can't recall the exact numbers but IIRC the generics could range as low as 10mg per patch were as the "best" brand had 16.2mg per patch. I could be wrong on the numbers as it's been quite a long time but regardless there were large differences in total Fentanyl content. Considering the users I knew would extract the patches & IV the large variations in Fentanyl content made an already dangerous practice all the more dangerous. I'm starting to digress & ramble though I think.
I'm not that familiar with lethal injection practices but to the best of my knowledge Fentanyl is used in some states lethal injections. IIRC it was first used in lethal injections in 2018 in the state of Nebraska. IIRC the states of Ohio & Nevada were also looking into using it. As I mentioned I'm not that familiar with the topic but to the best of my knowledge it is used in some states. As far as I know lethal injection protocols are public information & if you wish to find more information regarding the drugs used it should be available. Regardless; hopefully my answer has helped to elucidate & you have a little more insight into your question.
Just noticed that I think you may have missed a 0 when typing out the concentration.

The usual concentration for vials is .005mg/mL. 50mcg/mL is the most common concentration for the vials to the best of my knowledge. In the USA anyway. My apologies if the concentration is different in Peru.