I just noticed there's shown of minutes next to player in galaxy screen. Does that mean when last time a player login or when last time I sent scout?

It's the last time that there was activity on that planet.

An asterisk (*) means there is activity on the planet RIGHT THEN. Which could be things being built or a recent fleet arrival/departure or probing.

After a period of time without activity - and I'm not being evasive, I'm not sure how long - the timer will start. At 60 minutes, it goes away.