does an attorney charge his client a fee for putting a public notice in a news paper,or in the classified ad''s? Is it required by law?

It is a legal requirement that notice be "published" to give notice to any unknown creditors of the decedent.  There is a cost to publish this required notice.  In IL, where I practice, the charge for the usual publication used is $190.00 and yes I require the client to pay this amount.  I typically do not charge for preparation of the publication paperwork in addition to the publication costs, but some attorneys bill anything that takes more than 6 minutes.  Hope that helps.