Slitherine

both are formations.can you effectively be in both formations? can skirmishers shoot like extended line?

Yes. Although not very well.
The extended line shooting bonus is only for close range, where each half of the extended skirmish line gets 3 dice on a- poa.

The extended skirmish line still only gets 5 dice all up at medium range. And of course drops a dice when taking CTs for being in a single rank.

is there 'extended line skirmish'? formation, 2 *2 units goes to 1*4 skirmish is this a formation change?

There is such a thing as an extended skirmish line, 1 base deep by 4 or 6 bases wide. I have used it with my Grenzers lots of times. Downside is if you get charged try to not burst through friends out back with your evade.
Changing from single line to 2 or 3 deep skirmish formation is a formation change, same as changing from skirmish to tactical or vice versa.

Normally I start my lights in an extended skirmish line to block as many second moves as possible, and to screen more troops out back.