The answer is complicated, but basically boils down to yes, kind of.

When an atom absorbs a photon and one of its electrons becomes excited, it will gain mass. Not a lot. Essentially insignificant, but technically it gains mass. So in this way, yes, the energy from the photon was converted to mass.

The energy that the electron absorbed from the photon to move to a higher energy state doesn’t change the mass of the electron, but it does change the mass of the overall system (the atom), because the mass of the atom includes the rest mass of all of its parts plus any kinetic energy they have.

Actually, this happens any time a photon is absorbed by any system. When light hits your skin and makes it warm, your mass is increasing. Again, by a very insignificant amount, but technically the light is adding to your mass.

Also when something emits a photon, it loses mass.

As far as just converting the energy of a photon into a massive particle without another particle absorbing it, I don’t know of any way that’s possible.

See: https://en.wikipedia.org/wiki/Invariant_mass

According to relative theory, energy and mass are interchangeable, so yes.

An example is quark confinement, if you want to split quark from neutron or proton, you need energy, but even you cracked them out, the energy would form another quark, so you can't see single quark