You also appear to have some cables that are coming off the panel, after the main breaker, but not protected, ie no breaker. Hmmm.. Do you have a sub panel somewhere?
I think you need professional help. Those smaller wires coming off the lugs right under the main 100A breaker could overheat w/o the 100A breaker throwing. I don't know where they are going, but they are a fire waiting to happen.
1. Can I do it myself or do I have to hire a certified electrician (IL)?
The fact you are asking means you don't probably know enough to do it yourself.
2. Is it just the box that needs to be replaced, or does something else need to be done?
See above. (Probably needs a lot more. May need heavier cable from the pole, heavier cable from the meter to the main panel)
You will need someone to pull the meter to replace the panel with a 200A service. Generally no one pulls a meter unless they are licensed cause the utility really frowns on meter pulls by novice folks. There are folks that are unlicensed that pull meters, but they are experienced and know the details. You are probably not-- based on my appraisal that you did not explain those unprotected wires. And I think you need more research about a grid tie system. Start with talking or looking at what your utility has online. First online. Then call. Do they allow grid tie? What is their permitting process? They will put you on a different rate plan sometimes...