As all mass has gravity is there a limit to how far from the object the gravity can be detected for instance is the sun's gravity infinite?

"As all mass has gravity"

Better to say this as "As spacetime is the product of all mass..."

"is there a limit to how far from the object the gravity can be detected for instance is the sun's gravity infinite?"

It is a detection limit only. With the expansion of the Universe, "galactic superclusters" are the largest gravitationally bound structures. So in some sense, you could say that gravity does not survive much beyond the size of a supercluster (like the Virgo supercluster, to which we belong).

It isn't like gravity-from-mass stops, but more like the "pull-of-entropy" dominates. They are both the shape of spacetime.

Gravity detection equipment has limits to it's sensitivity, however according to Newtons law, a gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. Consequently at any distance, even infinity, there would always be some calculable gravitational value, since the product of the two masses remains the same. It may certainly be too small to have any measurable effect at large distances, but it is still possible to calculate it.

yes. This is a property of graviton( elementry particle responsible for gravity) that their force doesnt have limit. If for instance you some how bring a new planet and keep it between mars and earth then its effect will be felt by the whole solar system at hte same time through out the universe.

Hope it helped

CHEERS