Can I stick a tarpaulin using a nylon Velcro(Hook and Loop) in my wooden roof?
Four questions, but the one that's most important is the last one. The rest of the questions do not matter if the answer to the last is negative.

Hook and loop fasteners have the greatest strength in shear, forces applied in a sliding-across manner. If you had need to hang the tarp vertically on a wall and all the other aspects were solved, the fasteners might work if sufficient numbers/length/area were used.

Hook and loop fasteners are removed by applying force in tension, the stretching-away action of peeling them apart. In the case of a tarp on a roof, any appreciable wind is likely to get under the edge of the tarp and peel the fastener free. When the peeling begins, additional area is exposed to the wind, accelerating the action, allowing more peeling at a faster rate.

Using stitching to attach the fasteners is mechanically sound, but the thread used to perform the stitching is to be considered when calculating exposure life. One can have fasteners that will last for a year in the sun, but the thread can fail if it is not sun-fast.

If you are able to secure the hook and loop fastener to the very edge of the tarp, it would likely mitigate much of the peeling, as there would be a smaller area on which the wind would be acting. It would require that the entire perimeter be "enclosed" in the fastener material, or some other means of sealing out wind forces be employed.