Can I read the part of Tafsirul Qur'an which is written both in Arabic and English without Wudu? Can I read it lying on bed?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

All Muslim scholars are agreed that the recitation of the Quran is permissible for the one who is in the state of minor ritual impurity that can be removed by ablution only. Imam An-Nawawi wrote in his book Al-Majmoo’: “The recitation of the Quran, while one is in the state of minor impurity, is permissible, according to the consensus of all Muslim scholars, though it is better to perform ablution for that purpose. As for touching the Quran (only text) without being in the state of Tahaarah (purity), the majority of scholars, including the four Imams, are of the opinion that it is not permissible to do so as Allah Says (what means): {In a Register well-protected; None touch it except the purified.} [Quran 56:78-79]

And for the Hadeeth of the Prophet who wrote in a letter to ‘Amaar ibn Hazm: “No one should touch the Quran except the one who is in a state of purity.” [Ad-Daaraqutni; Imam Ahmad based his opinion on this Hadeeth]

Imam Ibn Taymiyyah said: “Imam Ahmad said, ‘No doubt that the Prophet () wrote the above words in his letter to Amaar.’” Salmaan and Ibn ‘Umar are of the same opinion and we do not know anyone from among the Companions who opposed them.

As for touching some explanations (interpretations) of the Quran, the ruling is that if the original text of the Quran is more than the explanation, then it takes the ruling of the Quran itself. Imam An-Nawawi said: “If the books of explanation of the Quran contain more text of the Quran than the explanation then it takes the ruling of the Quran itself, such as the books that explain only difficult words of the Quran. If the explanation exceeds the text of the Quran, then one may touch it without ablution. The same ruling applies to any translation of the Quran.”

With regard to reciting the Quran while lying on a bed, it is permissible as Allah Says (what means): {Who remember Allah while standing or sitting or [lying] on their sides.} [3:191]

The Quran is also a form of Thikr. However, scholars prefer that the recitation of the Quran be in a good position, facing the Qiblah.

Allah knows best.