How have astronomers deduced the size of the Oort Cloud?

in a sense, yes,in terms of numbers of objects no, each white dot is representing an object. However in real terms each dot on the picture is massivly oversized compared to the object it is representing. read more

It's estimated based on the maximum distance from the sun of long-period comets. read more

By "Oort Cloud" we usually mean the part of this soup beyond our Solar System and out towards other stars. The Oort Cloud has no defined outer boundary. For convenience it can be assumed to extend half-way towards the nearest stars, which are about 4 light-years away, so its radius would be about 2 light-years. read more

The outer Oort cloud may have trillions of objects larger than 1 km (0.62 mi), and billions that measure 20 kilometers (12 mi) in diameter. read more