According to our Forum Rules (red link near the top of the page), we cannot help you until you show us your attempt or give your thoughts. You could start by finding the pKa values. You are correct that amides do not ionize under typical conditions.
You must be a fellow Badger, I assume?
1. So with Melphalan, we have two different amine groups which have a pKa of roughly 10.5ish (protonated). Since the pH is 2.0, it's in an acidic medium and the pH is less than the pKa of the amine groups therefore the amine groups get protonated. The carboxylic acid has a pKa of around 4 therefore the pH is less than the pKa so the H stays on. Is this correct?
2. I believe alcohols, phenols, and the amide in amoxicillin will not ionize therefore what we have left is an amine group, a carboxylic acid, and a sulfide, all of which will ionize. The amine is basic, the carboxylic acid is acidic and the sulfide is acidic. Is this correct?