Been seeing a lot of misinformation and inaccurate details in regards to Frank's addiction. Obviously in things like fanfic it doesn't have to be precise nor is it a medical text, and there are some things depicted in the show that don't quite make sense either. But if you are curious, confused, or want to depict benzodiazepine addiction with more accuracy, then here are a few pieces of information that may help:
Frank was mostly likely prescribed something like diazepam to treat muscle spasms around his back injury whilst healing, and long term use has left him with a physical dependency. Benzos are prescribed on a "as needed" basis (think how ativan is used to stop a seizure, or valium to calm an episode of a panic disorder), and when prescribed in cases of pain management are recommended for use up to four weeks, and no longer. Although sometimes prescribed in pain management, they are not analgesics.
Benzos are a CNS depressant and controlled substance. They wouldn't give a traditional "high", instead it would be a sedated state of relaxation (if you've taken valium or xanax before, those are benzos). High doses can induce amnesia and blackouts.
The way Frank spoke about his injury suggests that Robby was around when it had happened, placing the injury sometime during his residency, so anywhere between 2-1 year/s ago. (edit: this injury was most likely a herniated disc).
He most likely justified stealing from the hospital as withdrawal symptoms include physical tremors, cognitive impairment, anxiety, and agitation, and so working with those symptoms would put patients at risk.
Diazepam is sometimes used in the treatment of certain symptoms of opioid withdrawal, but this would be done in like peak withdrawal under the supervision of a doctor so it's very unlikely this was the case for Frank. There are more medications and tools to treat opioid addiction, and the withdrawal from opioids, although unpleasant, is not as dangerous as the withdrawal from benzos. Benzos are sometimes used to treat alcohol addiction but withdrawal from alcohol lasts up to seven days, making developing a dependence on them during this time unlikely.
Benzo withdrawal is fucking nasty. Going cold turkey is not an option, and any attempt to just "sweat it out" can be life-threatening. So Trinity figuring it out just may have saved his life.
Going to a rehabilitation facility for withdrawal due to medical use does not seem the appropriate response as these facilities usually focus on individuals who take substances recreationally (edit: forgot to explain, a doctor would first asses the severity of addiction and decide what is the best course of action: referring you to see a specialist or clinic as an out-patient, or admitting you to a facility). However, he still went, as per the conditions Robby set. At least in a facility he could withdraw under constant monitoring.
Either way, going to a rehab facility or hospital for addiction is a really fucking traumatic experience. If you've never been I don't quite know how to explain it, but trust me it is. It will also take a little for Frank to recover from the experience of it.
If Frank truly was trying to wean himself off (which is possible, chloradiazepoxide (librium) is used to treat benzo withdrawal), then it would be another four weeks to safely taper the dose down to zero (if he was not, then 6-8 weeks), and then another two months after that for the acute withdrawal symptoms to stop. Some symptoms may persist for years after.
After leaving the facility, Frank would still continue to get treatment as an outpatient, which would include counselling and physical check-ups. He would get most of the psychological support during this time, and not whilst actively withdrawing, as the patient actually needs to be in a headspace receptive to therapy. Being an outpatient can last from six months to a year.
There is no rule saying that you can't take other substances or drink alcohol while recovering, however it is very, very strongly discouraged, and research shows that those who drink are more likely to relapse.
He would still be allowed to take over the counter painkillers. Idk why in a lot of fanfics Frank cannot take even paracetamol. He can take them and suffering in pain would only increase the risk of relapse.
Chances are he would be prescribed melatonin to assist with sleep and ease some of the withdrawal symptoms.
Cannot stress this enough, benzodiazapine withdrawal is fucking horrific. Symptoms include anxiety, weight loss, paranoia, dissociation, paraesthesia, muscular spasms and cramps, sweating, panic attacks, diarrhea and vomiting, depression, increased sensitivity to sensory stimuli (light, touch, sound, smell), agitation, dizziness, hallucinations, and insomnia, amongst others. These are symptoms that show up when weaning off, and remember, they last two months after the last dose and some can linger even up to a year later, and some even years after that. If you stop taking benzos all at once, the symptoms are worse (seizures, mania, psychosis, aggression, delirium, overheating, coma).
Whether or not Frank was aware he is an addict in s1 is a matter of interpretation. He clearly had some idea that things were wrong, but whether he was aware of the full extent of his addiction and risk to his life is not definite.
Whether or not Frank would "crave" benzos after recovery is also up to interpretation and dependant on triggers, but I think it's fair to assume that moving forward he would probably want to avoid benzos even if medically recommended (due to the mechanisms of benzo addiction, each subsequent withdrawal is worse). He may find himself craving them when experiencing prolonged withdrawal symptoms, he may have cravings when experiencing pain. He may not have any cravings at all. I know people who have been sober for years but still have cravings, and I know people who recover and never look back. I know people who never touch what they were addicted to ever again, and I know people who can take things recreationally without fear of relapse. The definition of "recovered" can vary from person to person. There is no scientific calculation to work it out.
If I made a mistake here please let me know, I like learning. Anyway, hope this helps :)