What really is a particle? How can massless particles exist? How can it still be a particle if it doesn’t have any mass?
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I believe there are some misconceptions in your question:
1. Massless usually refers to it having no rest-mass i.e. not having any mass when the object is at rest. If an object however possesses kinetic energy or really any momentum, then according to Einsteins equivalence principle it also has mass. Since light has an energy of E=hf you can also assign a mass to it since mass and energy are two sides of the same coin.
2. As to what really is a particle? Well thats a bit more of a complicated question. Particles used to be defined by their charge, energy, shape, position and momentum, however that point of view is a bit outdated. At small scales particles tend to lose some well defined properties such as their position and momentum. For example: An electron has a well defined energy value around a nucleus, their position and momentum however are not well defined. Only once a physical process imposes certain boundary conditions on this system (for example an observation), the electron has a well defined position (or momentum; it cannot have both at the same time with arbitrary precision: see Heisenbergs uncertainty principle). There are numerous interpretations as to why particles behave that way, however since all of those make the same predictions and cannot be distinguished from one another experimentally we assume all of them to be equally correct.
Now as to what particles really are: According to our best model of standard physics (which is incomplete btw), each particle corresponds to a certain symmetry of our physical reality. Im still in my bachelors and havent had the honour to study the standard model in detail yet, so I unfortunately dont understand that part fully neither. Keywords for this are Gauge Symmetry and Poincare Invariance.
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