1. Namaz-e-janaza is Farz/sunnat?
2. Is It lawful to wear shoes during Namaz-e-janaza?
Answer:
The Janazah prayer of a deceased Muslim is a communal obligation (Fard Kifayah). If someone is buried without it being performed then the whole community is held responsible but as long as some gather and perform it, the obligation is removed from the whole community. (Maraqi Falah p.213)
With regards to your second question, Shaikh Molana Ashraf Ali Thanwi 
has written the following in his Beshti Zewar (p.195)
“These days, some people offer the Janazah prayer with their shoes on. For them it is necessary that the spot on which they are standing is pure, and that their shoes are also pure. If they remove their shoes and stand on them, then it is necessary that only the shoes be pure…”
The conclusion we can come to is it is permissible to pray the Janazah prayer while one is wearing shoes provided they are free from any impurities and najas.
It is narrated from Said bin Yazid Al-Azdi who says I asked Saaiduna Anas bin Malik 
whether the Prophet of Allah 
had ever prayed with his shoes on. He replied, “Yes.” (Sahih Bukhari)
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham.