Quote
When performing Ardas outdoors is it compulsory to: - remove shoes in any weather conditions?
As Bhai Jasjit Singh pointed out, it's better to remove your shoes irrespective of the weather, however, if some is physically challenged for whatever reason, then's we must realize that Guru Sahib is Jaani-Jaan and in such circumstances it's okay if such person keeps shoes on. Normally, everyone must stand in Ardaas but if someone is unable to stand due to one's physical condition, then Guru Sahib is always Merciful and Forgiving.
Quote
- touch the ground with hand or matha tek at the conclusion?
Touching the ground with hand while bowing is fine. In many cases, the ground surface may not be clean and may even have tobacco products or other impurities. In such circumstances, there is no compulsion to touch one's Dastaar and forehead on the ground.
Quote
Also is reading Dohra required if doing Ardas at home or should it be read only in Sangati roop? Finally who penned the Dohra?
Agya Bhaee Akal kee including Raj Karega Khalsa is Gurbani. Guru Sahib did not record this in written form because this was done Uchaaran at the time Guru Sahib was about to Jyoti Jyot Samaa. Gursikhs present over there immediately memorized these Gurbani Bachans and then Gursikhs like Bhai Nandlal jee have recorded these words of Guru Sahib. So it's a must to sing these Dohras at the end of Ardaas in the Hazoori of Siri Guru Granth Sahib jee and if Degh is to be distributed. At other occasions, one can skip singing these Dohras.
The Dohras Vaheguru Naam Jahaaz hai and Khanda Ja kai Haath mein are wonderful words but are not Gurbani and were not uttered by Satguru jee. So many Gursikhs don't sing these at the end of Ardaas. But again, sky is not going to fall if these Dohras are sung. Singhs in olden days also used to sing "Dilli Takhat par bahegi, Aap Guru kee Fauj" but stopped singing perhaps due to pressure from the British. This particular Dohra definitely seems like Guru Sahib's Bachan because Guru Sahib jee's Fauj will in fact sit on the Delhi Takhat one day. Hopefully we can see such Bol-Baale of Siri Khalsa jee.
Kulbir Singh