Yes you can safely burn rolled up newspaper in your fireplace when you roll them up tightly using a newspaper log roller and water and soap.
My parents had one of those newspaper rollers that made logs out of newspapers and my dad would sit in the house watching Television and roll up newspapers into logs to make fireplace logs for the winter.
They worked pretty good.
You can also get the draft going in the Chimney of your fireplace by lighting a newspaper and holding it up the chimney which will help to get the chimney warmed up so the fireplace will produce less smoke when lighting it.
You can also buy pressed manufactured fireplace logs as well which is made from recycled wood scraps.