Is this a viable solution to way to avoid the effects of climate change? It's unrelated. The whole thing is to emit less carbon. If the dome does that, then yes.

Would it be cooler in the dome? Dude, domes are very cool. That's why chrome-dome is such a compliment. In terms of temperature, probably not. Heat needs to dissipate, and any sealed area is going to maintain thermal momentum more than an open space. Unless you started out cold, then it would stay cold for longer than an open space.

Would there be any negative repercussions? Yes. But you'll have to be more specific. It would be a huge undertaking that probably wouldn't be possible, emit lots of carbon, probably be protested by a lot of people, huge waste of resources, etc etc. Not to mention this experiment has been attempted many times and never been successful.

Would clouds form inside the dome? Could it rain in the dome? If it was big enough, and therefore yes.

Would the rain be more toxic than usual because car fumes wouldn’t dilute as well? How big do you want this dome to be?? It would have to be absolutely massive to make it worth having cars inside.

Could outside lightning break the dome if it got struck? Well, it's going to be pretty thick isn't it, so unlikely. It would blacken and melt the glass over time. But at the scale you're suggesting, it's essentially a mountain that would peak above the clouds.

Would there be a single point in the dome that the sunlight would be directed to that everyone would just have to avoid, else they just burst into flame? As .. fun as it would be to be smitten by the sun, I expect the glass would be so thick, it would be quite dim inside so, I don't think so.