Yes, Muslims believe that Islam is the perfect religion.
Allah swt said in the Qur'an, that He perfected the religion.
Of course, the Qur'an is perfect as it is the word of Allah, the All-Knowing Creator.
Here, I refer to the Shia school of thought:
Yes, the actions of the Prophet were perfect and everything he said as well, as he acted and spoke by the will of Allah swt.
One hadith of the Prophet, regarding transcribing his sayings, says:
[...] They said to him: "O Prophet of God, we hear things from you, should we write them down? He said: "Yes, by all means, write them down. By thy Lord, everything that comes out of my mouth is the truth."
(Ibn Uday, Taqaid al-Ilm, 73)
- The definition of perfection in regards to the Qur'an is, that it is the unaltered words of Allah swt, the truth.
In regards to the Prophet, perfection means infallibility. He was the perfect role model and example for mankind.
The interpretations of the holy verses are not perfect as these are mostly done by "normal" human beings, who might be scholars and therefore learned but nonetheless not perfect.