Does Allah (SWT) still show love and mercy to the people that disobey and disbelieve in Him?
There is a difference between Rahmah (mercy) and Muhabbah (love).
The Rahmah of Allah is for everyone believing and disbelieving (in this world):
"My mercy encompasses all things" (7:156)
That is the meaning of the word Ar-Rahman. Everyone is provided for in this world through Allah's mercy, and everyone is given an opportunity.
However, the mercy given by Allah to believers as opposed to disbelievers is different. The mercy to believers includes the blessing of Eemaan and forgiveness in the hereafter.
The Muhabbah of Allah as opposed to his Rahmah does not apply to disbelievers. Allah says in the Quran:
Say, "Obey Allah and the Messenger." But if they turn away - then indeed, Allah does not love the disbelievers. (3:32)