Split: What rewards does a Tablighi get?

Personally, I still take it as they are exclusive for jihad, however that doesn't rule out their use for tabligh as mentioned by the great ulama.

5. Why do Tableeghees use Ayaat of the Qur'aan & Ahadeeth which refer to Jihad for encoraging people to go in Tableegh?

Is it permissible to go out in jamaat and label it as "fesabillilah" (since some people say this word can only be associated with going for war)? What is the evidence for using Jihad verse for this work?

Allah Taala states in the Quraan: And struggle for the sake of Allah as it is required. Anas reported that the Messenger of Allah said: Whoso goes out in search of knowledge, he is in the path of Allah till he returns. (Tirmizi)

In view of the above, it is permissible to go out in Jamaat as this is also fee-sabeelillah and this has been emphasised in the Quran. Fee sabeelillah includes all kinds of efforts and struggle, e.g. tongue, pen, money, body, etc. [Kanzul Ummaal vol.10 pg.15]

You are free to give dawah to non-muslims. But not from TJ platform.