Painkillers and antibiotics...

for 2 - Naproxen
for 1b - Flucloxacillin 500mg https://en.wikipedia.org/wiki/Flucloxacillin

1a - no clue.

1b - Cipro or Levaquin are fairly heavy hitters in the non-penicillin relative range. Both are broad spectrum, though I don't believe either is commonly used for MRSA-type infections, while Flucloxacillin is - however, Flucloxacillin is not a broad-spectrum antibiotic. The difference being - broad spectrums act against a wider range of bacterial families, while narrow-spectrum antibiotics have a more limited (and more targeted) range of bacterial families against which they are effective.

2 - depending on the severity of pain and injuries, and the attitude of the treating doctor. Naproxen is Aleve - works like Motrin/Ibuprofen, available over the counter as well as prescribed. It's non-narcotic, and non-addictive, and very commonly suggested for mild pain management. And no one would ever be afraid of getting addicted to it.
Something that might have been prescribed for more serious pain/injuries - vicodin/hydrocodone. It is addictive, usually used for moderate levels of pain management, and would come with the "don't want to take this..." for side effects, addictive qualities, etc.

Los Pollos Hermanos said:

Big thanks!

Update: Found info stating maximum daily dose for the yellow Percocet pills is 6 per day.
However, what would happen if he sneaked an extra one or two?

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Rather depends on his build - think about dose per kilo of body weight. If he's a big guy then a couple more are unlikely to give him a problem, if he's smaller.....

Los Pollos Hermanos said:

My "worry" is that Percocet contains paracetamol (acetaminophen), which ain't good for the liver in high doses. Same applies to Vicodin.

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That's why the maximum dosage is there. The recommended and dangerous doses of acetaminophen are pretty close together. Many cases of acetaminophen poisoning are due to combination narcotic abuse. So if the character often takes a couple more than the max, his liver and kidneys might just fail in a spectacular fashion and cause a pretty unpleasant death (which is why the FDA doesn't much like Vicodin and Percocet.)

Los Pollos Hermanos said:

Are there any painkiller pills out there which DON'T contain paracetamol/acetaminophen?! I need him to be taking more than he should for a few days. He has to get rid of the first stash in a hurry and then track down a new supplier for 3-4 more days of pharmaceutical relief. Would oxycodone fit the bill?

Ahhhh, the joys of fiction...

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Oxy works and is frequently traded under questionable circumstances. (Most drugs like those are more commonly known by their most prominent trade name, which is case of oxycodone is Oxycontin.) Also hydromorphone (Dilaudid), oxymorphone (Opana) or tramadol.

Not that I'd recommend it, but my mom takes oxycodone and from what I can gather, it's one of the stronger opioids in pill form. All damage the liver though at some point, so if that's a concern, I suggest your character invest in cannabis or salvia. xD

I have a severe chronic pain condition, plus I get migraines. And I'm allergic to Tylenol, and can't take Aspirin because it kills my stomach. Let me tell you, it's hard to find pain medications that don't include Tylenol or Aspirin! But there are options. For regular pain (not headaches), there's morphine sulfate (extended release), which lasts either 12 or 24 hours, depending on which type you get. It's generally given to people with chronic pain, though, not acute pain. For short-term use, Oxy might be prescribed. It only lasts 5-6 hours before wearing off. (I believe it's actually Percocet, but without the Tylenol. I could be mistaken, though.) There's also Fentanyl patches, which stick somewhere on your body and release the medication slowly, over a couple days. But Fentanyl can cause nausea and other side-effects, and if you have sensitive skin, it can cause problems, since it's a patch. There's also dilaudid and tramadol. My impression is that tramadol is a milder pain medication, and for some people, it doesn't do much, but dilaudid is stronger. It's what they gave me following my gallbladder surgery, since I can't take IV morphine. I was still in a LOT of pain, so I don't know how effective it really is, but supposedly it's "good stuff." Just not for me, apparently.

When they gave me dilaudid a few years back--I forget what for, possibly when I had pleurisy (an extremely painful lung inflammation)--it caused me to hallucinate. I don't remember what I saw, but at least I knew it wasn't real. The first time I ever hallucinated, when I was a teenager, due to one of the (non-pain) medications I was on, I saw a line of cartoon animals prance into my room. There was a cat, and he had mice riding on his back, and they were dressed like circus performers. I knew they weren't real, because they looked like chalk outlines, drawings that had come to life. It was bizarre, but very imaginative! I was worried when they gave me dilaudid after my surgery, but nothing happened, thank goodness.

If he was in a car crash, wouldn't he need a tetanus shot? (U mention a head injury - was there bleeding?) And I think the broad-spectrum antibiotic would depend upon the region, and the infections commonly seen there (Amp/Cipro/Cef), and on the occurrence of resistance (keeps changing every few years)
I think Vicodin or Morphine (don't know about Percocet) if you want something addictive. Also troublesome it would be if the drug has to be injected (I remember Cuddy injecting Dr. House!) Guess u'll need to consider side-effects...

Just FYI, Vicodin is no longer available, at least in Indiana. You'll need to check if it's available where your character is. Neither is Lortab. The current hydrocodone/acetaminophen combination is Norco, available in hydrocodone strengths of 5, 7.5, and 10.