Carpet

It is recommended for the followers of Ahlul Bayt (AS) to pray in any Masjid with any Muslim sect. This does not mean to pray like them even if the act is wrong according to authentic evidence, Folding hands in Salah was never done nor approved by the Prophet Muhammad (SAWA). Maliki Sunni sect do not fold their hands in Salah. None of Sunni Imams claimed that folding hands in Salah is Wajib or Fardh. Authentic evidence says that we should never fold our hands in Salah even when we pray with non Shia Muslims. Taqiyya situation is different when you feel a risk or danger on you, then you can pray like them to save yourself or other believers.

Same situation is regarding Sujood on the carpet which is against the teachings of the Prophet Muhammad (SAWA). In Bukhari, the Hadeeth from the Prophet : Earth was made for me as a place of propstration, and as a place of purification (Tayammum).

Wassalam.

Sajda (Prostration) on carpet is Not permissible unless you are under dangerous situations where Taqiyya becomes permissible for you to avoid possible danger or harm.

Wassalam.