ewaybill qery

Yes, e-way bill is required to be generated even in case of movement of goods within 10 km. The relaxation updating part B (vehicle details) is given only in cases of movement of goods from the place of business of consignor to the business of transporter for further movement of such goods, Therefore, in all other cases, e-way bill needs to be generated even if the distance to be covered is less than 10 km.

Yes , Eway is mandatory if value exceeds 50k, & movement is via motorized conveyance
You have genrate eway on delivery challan

Pankaj sir is right.
Using delivery challan, eway bill can be generated.