Fixed effect Model

dear all,

I am having problems with the fixed effect model.

In a nutshell, I am analysing the impact of disasters within families with regard to their health. Therefore I am doing a within household comparison, between the children born before the diaster and after, in the region hit and a control region (not hit). (before the FE model I do a D-in-D, but this is an other story).

I would like to add the formula for the fixed effect model. In the appendix, you can see what I did so far. But I am not sure it is right.
Further, when I run the model, I see that the constant is significant. How do I interpret that? (the data comes from dhs, robust standard errors, clustered at primary sampling unit).
Is there a problem of incidental parameters? How do I descrie that?

I really hope that somebody can help me!
Best wishes and have a nice day,