What are the 4 fundamental forces of nature and what connects them together? How do they interact together?

We are familiar with gravity, which acts on the property of a body known as mass. It is a force of essentially infinite range, meaning masses at very great distances will still interact. It's strength varies inversely as the square of the distance between the masses, and it is always attractive. Therefore, all masses attract all other masses.

(Note: I am describing gravity as it was known to Newton. This is not a general relativity treatment.)

Electromagnetism is similar to gravity is some ways. It also varies as the inverse square of distance, although the property that it acts on is charge. It can be either attractive or repulsive, and so, its effects will often be cancelled out, even for large collections of charge. E-M force, like gravity, also has infinite range.

In modern theories, this force is described as a gauge force, meaning there is a particle (called a photon) that "mediates" the force - the charges actually exchange photons as the basis of how the interaction works.

In your question, you ask how these forces interact, but in fact they do not! Gravity and electromagnetism are distinct and separate, although, like any forces, one can be applied to oppose or support the effects of the other.

The same is true of the two nuclear forces, They are both gauge field forces. However, the range of these forces is very short. Hence, they are limited in their effects to the nucleus of the atom.

The exchange of particles that occurs in these forces bring about changes in the nature of the particles on which they act - quarks in the case of the strong force, and quarks and leptons in the case of the weak force.

The weak force utilizes massive particles known as W and Z bosons to cause quarks to change their "flavour" meaning the "up" "down", "strange", etc characteristic. This is able to cause an up quark to become a down quark (or vice versa, depending on the W involved), meaning that at the same time, a proton becomes a neutron, and the affected atom changes into a different element.

The strong force holds quarks and nucleons together, with a mediating particle called a gluon. It acts on the "colour" of the quark.

That's probably enough info for now. You should draw your own conclusions as to whether the above connects these forces together in any manner. The gauge field nature comes to mind as one example of this.