Answer
(Fatwa: 1061/D=221/K=1431)
(1) Yes it may be sent for the purpose of teaching and preaching not for entertainment and play.
(2) You should try to keep your paint above the ankles in general conditions; because hadith severely warns against it; otherwise at least he should fold it while offering salah.
(3) عن ابى هريرة قال قال رسول الله صلى الله عليه وسلم من صلى بعد المغرب ست ركعات لم يتكلم فيما بينهن بسو ء عدلن له بعبادة ثنتي عشرة سنة . رواه الترمذي (مشكوة 104)
(4) In Mishkat page number 117, there is the detailed hadith of Hadhrat ibn Abbas (رضي الله عنه) which has been narrated by Abu Dawood, Ibn Majah and Baihaqi. Also Abu Rafe (رضي الله عنه) has narrated similar hadith in Tirmidhi in which the holy Prophet Muhammad (صلى الله عليه وسلم) taught his uncle Hadhrat Abbas (رضي الله عنه) the detailed method of Salatut al-tasbih, and informed him of its virtues.
(5) It is against etiquette and makrooh to do so while one has kurta.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband