You've already been told, it is how your skeletal muscles work. They pull on your ligaments which attach the muscles to your bones, thus pulling said bones.
Like any other force is "transmitted", by material or by the properties of space-time. For the material application an external pulling force results in stress and strain on the material that we can measure as an extension in length and/or reduction in cross sectional area. For an internal pulling force (say as a memory metal going back to its original shape, an extended spring going back to its rest shape or just muscles contracting) the opposite applies. There is a contraction in the length and a related increase in cross sectional area (for the extended spring case it is just a release of the extension stress applied before).
For space-time applications, like electromagnetism and gravity, attractive forces are generally considered pulling and repelling forces are generally considered pushing. It is a nomenclature based on convention but one related to the energy of a test particle in the field.
Nope, you just forget that this has been explained to you before as has the irrelevance of belief.
As already explained to you, curved space-time, as tidal forces, results in both net compressive and expansive (pushing and pulling) forces at the same time.
EternalHope.