Last login

Hello,
It is possible (but depending on your profile and rights, you might not be able to see that screen).
Anyway, as an administrator, look for "Tools" in the left menu, and then "Audit connections".
You'll see a screen of all the current connected users.
Use the closed switch on top right corner of the list area and you'll get all the past connections for any user. Then use the filter to find your given user.

1. Is it possible to get this information by API ?

Yes, request API for object "Audit"

2. Is there in PQ any functionality/plugin to block inactive accounts due to selected policy (for example no login after 1 week => lock account)

No, blocking is possible only on number of incorrect connection tires, not on "no activity"