Try this for the not-quite-ripened fruits. First, don't squeeze them... you'll ruin an unripened peach by doing that. Next, place them stem side down on a muslin (not muslim) cloth or cotton napkins... don't use terry towels. Place them in a cool location well out of the sun but not a darkened closet or pantry. Cover them with the same type of cloth. The... walk away... just walk away. After about 3 to 5 days, uncover them and smell one... the nose knows. It'll smell strongly of ripened peach. They may need more time... maybe up to 10 days but it works every time.
Next... split seeds... there's a number of reasons for this, depending on whether or not they are "cling" or "free stone" peaches and whether they are eraly bearing or not. Most likeoy the culprit is a drought or at least uneven rain fall. It doesn't really hurt anything.
Here in the western U.S. many locations have exceptionally good conditions for growing peaches and the above information came from a friend who grows them commercially...