A toilet is a piece of sanitary hardware used for the collection or disposal of human urine and feces. Toilets can be with or without flushing water (flush toilet or dry toilet). They can be set up for a sitting posture or for a squatting posture (squat toilet).
Yes, it is permissible, as long as it stays protected from any kind of najasah contamination.
And Allah knows best.
Simply, everything is Taahir for you unless and until you know for sure that it is Najis. This is a rule in jurisprudence based on a narration of Ammar from Imam Jafar Al-Sadiq (AS) stating : Everything is ritually clean till you know that it is ritually unclean. (Wasaa'il al-Shia, V.2, Section 37 on Nijasah).
Your doubt in this matter does not make any difference. You are ritually clean because you are just doubting and not sure that your body became Najis.
We have covered the topic of waswasah and doubts in tahara a few times, and you are able to search in the Q&A on the topic of waswasah and taharah.
The simple rule of thumb is because you are doubting, you consider it all to be tahir. Nothing more.
Please watch this clip, which is a part of a lesson I gave on taharah and najasah. Hope it will be of benefit.
Yes it is permissible to recite Du'a and mention the name of Allah everywhere. We have a Hadeeth stating that Prophet Musa asked Allah: Can I mention your name when I am in a place where I feel ashamed to do so? Allah replied: O Musa, mention my name everywhere.
It is recommend to recite Sura Al-Qadr during performing Wudhu where ever you perform Wudhu.
It is permissible for you to recite supplications in English, if you wish. Of course, the ideal would be for you to recite them in their original language, as has been transmitted to us from the Ma'sumeen (a.s.), and memorising what you are able to. Along with this, you are able to look up the meanings, and the bonus for doing this is you are picking up wider vocabulary in Arabic language as well.
With prayers for your success.
Drops of urine which you know that it touched your body or cloth are Najis but not drops of water of washing when it does not have any part of the Najis material. Drops which are not noticed or too small to notice should not harm you because you don't know that it touched your body or cloth or whether it was drops of urine or water. Everything is Taahir for you until you know that it is Najis.
I will assume that what you mean by an "Indian" toilet" is a squat toilet, or a ground toilet.
While urinating, if drops of urine splash onto you, then of course it must be purified, but when you are washing, and splashes of water fall onto you, then it is fine.
To avoid urine splashing onto you, direct it in such a way where it doesnt splash, or pour water simultaneously.
As for "feeling", you only wash what you know for sure fell onto you, and nothing else.
And Allah knows best