Do dreams about the father's death—despite his kind treatment and the intense love for him—indicate a deficiency in faith, and what is the remedy for that?

Dreams do no harm, and no rulings are based upon them. If you see a dream you dislike, seek refuge in Allah from Satan and do not mention it to anyone, for it will not harm you. However, if you see a vision you like, praise Allah for it and relate it to those you love, and know that it is from Allah.