Yes. Try a mixture of clove and olive oil equal amounts and gently rub on painful areas using a q tip.
Yes. Teething is often blamed for periods of fussiness but it's hard to tell when it's really the cause. I'm fond of freezable teething rings that you can trade out as they warm up. You can paint benedryl on gums and get temporary numbing effect. Gels sold for teething but they occasionaly have side effects. All may just distract baby from another minor discomfort but if it helps, try it.
Massage, cold cloth. Gentle massage on your baby's gums will help relieve their pain. Also using a cool washcloth and allowing them to suck/chew on this can be helpful. Whatever you do provide them to chew on make sure it is not something that may cause choking. If your baby needs more pain relief tylenol (acetaminophen) may be used.