Am I allowed to study and read Ibn Qayyim's books without an Ustadh? What about reading ahadith and the Quran (translation)? What about tafsir?
Gaining knowledge has many venues, including learning through a teacher (sheikh, Arabic: شيخ) or from books without a teacher. The common point of any method is to ensure that the source (let that be a teacher or a book) is a valid one as Ibn Sirīn said:
إِنَّ هَذَا الْعِلْمَ دِينٌ فَانْظُرُوا عَمَّنْ تَأْخُذُونَ دِينَكُمْ
Indeed this knowledge is faith, so carefully consider from whom you take your faith.
There is no doubt that Ibn Qayyim al-Jawziyya is one of the greatest scholars of Islam in jurisprudence, tafsīr, and hadith. Suffice it to say that he was the student of Ibn Taymiyyah, and his students included Fairuzabadi, Ibn Kathir, and Ibn Rajab. Studying the works of Ibn al-Qayyim will actually cover all the areas you inquired about (including tafsir and hadith).
One has to keep in mind, though, that reading books may result in some faults in knowledge either through misunderstanding of the written text, overlooking the context, or a multitude of other reasons. One should always seek clarifications when in doubt, and one should keep in mind that even without ambiguity, one's understanding may still be incorrect.
Imam Abdur-Rahmān al-Awzā'i used to say that the knowledge about Islam used to be an honor that people learned from each other. When books came into the picture, those who are not qualified started to have an opinion.
The point of Imam Al-Awzā'i is that without a teacher, there could be potential errors that do not get corrected. The most dangerous ones are not when the person is not clear on the meaning of the text (they may eventually seek clarification); rather, when the person thinks they fully understand the text when in reality they do not. It is rather difficult to guess what the reaction of Imam Al-Awzā'i would have been to the Internet and Google.