We buy solarcoins with gridcoins through voluntary actions?

That was how I phrased it; there could be other mechanisms as well, but I opted for the simplest option for this proposal.

Apart of the direct bridge omitting bitcoin, which should be quite straightforward to do, what else we need for this idea to work?

That's it, as least as I described it here.

Also, both coins have lost close to 95% value since the peak a year ago. Rewarding anything is, at ~1M market cap for each, rather symbolic.

That's a really good point. However, I think that there's a danger in thinking about the future of Gridcoin limited to its current marketcap, since that argument could also extend to much of the other work that we're doing for the coin as well. We need to be aware that it's only ~1M, but plan like it's 100M.

What about if coins would merge into one and reward both crunchers and energy producers? Or one of the coins would also start rewarding what the other one does? This would be a more user friendly solution, as one doesn't need two running wallets and two sets of keys / backups to worry about.

I'm not sure how we could could merge two coins together. What do you mean? Regarding the two wallets/keys problem - as cryptocurrencies become more popular I think there will probably be other solutions to this problem, since it's not limited just to this scenario.

Another idea for offsetting carbon emissions: Run a BOINC based scientific or engineering project that solves some fundamental or design / construction challenges in green energy field (similar to DHEP).

We have a climate prediction project, but unfortunately it's not whitelisted since they don't update their stats often enough. I believe we also had a project that tried to improve solar panels design (similar to your last point), but I don't know much about it. Although finding such a project and crunching for it would certainly be a really good way to do that.