Can EcoFlow power stations be charged by solar panels and the 12V car cigarette lighter at the same time?

No, this is because the car charging and solar charging share the same input interface. (XT60 outlet).

Can I connect EcoFlow power stations to my house electric panel directly?

For safety reasons, Ecoflow does not recommend direct linking to house electric panel for it requires professional electrician skills. If you hope to integrate your Ecoflow power stations to house electric panel, please kindly check Ecoflow smart home panel.

https://ecoflowtechhelp.zendesk.com/