1.I would say yes. 10k is just enough for the funeral in the case of death. Additional life insurance provides surviving spouse some finance support. It is critical to the survivor if s/he does not work.
2. If your wife does not work you need higher coverage on your life. If bad luck happens to you she still have some income. How much is enough? It depends.
3. Usually group insurance costs less than individually purchased policy.
4. You need to check with HR of your firm. Probably you will be given the option to convert the group coverage to individual policy on the condition that you pay the premium.