Sometimes it feels like without electricity, life stops

We don't have programmed outages here, but we have periodic loss of power that can last for a week or more. During the last big storm, in 2012, we lost power for 13 days. Then I was relatively young--65--and handled the inconvenience OK. Hard, though because we had freezing snow during the outage and things got quite cold.

Recently I've decided it would be much harder to sit out a loss now. At considerable expense I've bought two portable charging batteries and a solar charging panel. I figure at least the refrigerator, an electric blanket and small appliance can be charged.

Doesn't sound like much, but as you say, it seems life does stop without electricity.

that seeing smoke like marks around that box (which is a connection point of several cables) is not a good sign

For sure!!! You are lucky the house didn't burn down. Do you have circuit breakers? These are supposed to 'flip' (turn off) when there is an overload, I believe.