Hello,
As per my Guru ji, you should not keep the Shivling in your home. Shivling must be in the temple. If you keep it at home, then you will face some kind of problems in near future.
Regarding the pooja, I would suggest you to do it after 5pm. Please don't do it after 12 as the time of bhoot and pret starts after 12.You can do worship after 5 pm.
Regards
Jai Babe Di