No Skype calls can go on for as long as needed. There is not cutoff or anything like that unless you are calling a mobile number. Then it cuts off when you run out of credits.

You can Skype on the downloaded program of Skype

You do not need your Skype number to make Skype to Skype calls. You can log into your Skype account with your recently made ID and password.

If you have created your Skype ID recently, then you will not your number to make Skype to Skype calls. You can log in with your Skype ID and password to make calls.

Yes, you can make Skype to Skype calls with just your ID and password, you don't need your Skype number.