Does Silent Gravestone stop eternalize
No. (Mostly)
Silent Gravestone's abilities read

Cards in graveyards can't be the targets of spells or abilities.
{4}, {T}: Exile Silent Gravestone and all cards from all graveyards. Draw a card.

The first ability prevents targeting in much the same way Hexproof and Shroud do.  So do embalm and eternalize target?
Embalm is defined as follows:

702.127a [...] “Embalm [cost]” means “[Cost], Exile this card from your graveyard: Create a token that’s a copy of this card, except it’s white, it has no mana cost, and it’s a Zombie in addition to its other types. Activate this ability only any time you could cast a sorcery.”

Eternalize is defined as follows:

702.128a [...] “Eternalize [cost]” means “[Cost], Exile this card from your graveyard: Create a token that’s a copy of this card, except it’s black, it’s 4/4, it has no mana cost, and it’s a Zombie in addition to its other types. Activate this ability only any time you could cast a sorcery.”

There is no mention of targeting in embalm and eternalize, therefore Silent Gravestone's ability won't affect them.
Generally speaking, an ability that only affects the card it is on doesn't target, while abilities that affect other cards do (unless it's affecting all cards of a specific type, like Silent Gravestone)
That said, Silent Gravestone's second ability will prevent players from embalming or eternalizing any of the creatures it exiles.