Does a person become an infidel if he dislikes a ruling among the rulings of the Sharia, yet acknowledges and knows that goodness and righteousness lie in Allah's judgment, while having an inner feeling of aversion towards some religious rulings, finding acts of worship burdensome, and having doubts about the existence of Allah and the Last Day?

The obsessive whispers have taken a great hold over you. You must ignore them, turn away from them, and live your life normally. This is what Allah has prescribed for you. You are not required to make up fast days because the default is that your fast is valid. As for the whispers concerning faith, turn away from them, and know that you are upon Islam and will not exit it because of these thoughts. Finding acts of worship burdensome is not a sign of hatred for them, and thoughts of doubt do not affect your faith as long as you dislike them. Repel the whispers and pay them no attention, for you will be rewarded for that. You are a lover of Allah's law, so abandon the whispers of Satan.