What exactly are force and momentum?

I cant wrap my head around what the actual idea behind these concepts is. It might sound so stupid. But I genuinely cant understand what a Force is. My thoughts are as follows:

Q:What is force?
A: Its the rate of change of momentum
Q:What is momentum?
A: Its mass x velocity.
Q:But photons have momentum and they have no mass so that can't be right, so what is momentum?
A:???

Also, the forces come as a result of 4 fundamental forces right? Gravity (Newton's Law of Gravity); Electromagnetic(Coulomb's Law); Strong Force (??); Weak Force(??). How do we know these exist and how do those laws work? Were they just simply derived because they work(i.e. the numbers fit and can make predictions so that all we care about)? Or is there something more fundamental that I'm missing?

[[Just a bit of background on me, I am actually a 1st year chemistry student, and in our Physical Chemistry Lectures we've been studying Coulombs Law in a Lecture course called The Physical Basis of Chemistry: The Role of Charge. And during these lectures I have realized that I don't really have a solid grasp of the classical mechanics behind any of it and don't really understand what a force actually is apart from a simple push-pull idea and the idea that it is a rate of change of momentum. But then I don't really know what momentum is (see above)]]

Kind Regards