wa 'alaykumussalaam and Eid mubarak
You can submit questions to
https://islamqa.info/en
or ask Sheikh Assim al Hakeem on twitter or his website, he is still answering questions daily so you get answered faster inshaAllah
https://twitter.com/assimalhakeem?lang=en
http://www.assimalhakeem.net/
As for praying in a room that has a toilet in the corner, according to islamqa.info it is permissible as long as there is a barrier/wall between the toilet and the area he prays in
So the idea to use cardboard is good inshaAllah and also to cover himself from his cell mate when using toilet and as barrier between toilet and the area he prays in
https://islamqa.info/en/answers/14506/praying-in-a-room-at-the-edge-of-which-is-a-toilet
It was narrated in a saheeh report from the Prophet (peace and blessings of Allaah be upon him) that he said:
“All the earth is a mosque except for graveyards and bathrooms.” (Narrated by al-Tirmidhi, al-Salaah, 291; classed as saheeh by al-Albaani in Saheeh Sunan al-Tirmidhi, 262).
“Bathroom” refers to every place that is used for the purpose of relieving oneself; it is not permissible to pray in any such place.
This room on the edge of which there is a toilet is not considered to be a bathroom so long as there is a barrier between it and the bathroom, with a wall and door etc.
In this case prayer in that room is valid, because the prohibition on praying in bathrooms is because they are usually naajis (impure), and this room is not like that.
And Allaah knows best.
If he can find another cardboard to use as prayer mat inshaAllah he can use as a prayer mat
https://islamqa.info/en/answers/213...-carpet-the-edges-of-which-reach-the-bathroom
If a person prays on a carpet, the edge of which is impure or in contact with something impure, or it is spread over something that is impure, his prayer is still valid, because he is not in direct contact with the impurity.
Ibn Qudaamah (may Allah have mercy on him) said: If he prays on a cloth, the edge of which is impure, or if there is beneath his feet of rope that is tied to something impure,
but what he is praying on is pure, then his prayer is valid, regardless of whether or not the impurity moves when he moves.
That is because he is not carrying the impurity and is not praying on it; rather his prayer mat is in contact with it. This is like if he prays on pure ground that is connected to impure ground.
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For muslims who are in prisons due to false accusations and injustices, may Allah ease their suffering, expiate their sins or decree them good as compensation for the hardship they and their family endure, and release them soon.