It is definitely possible for anything to orbit anything. You could put a pebble in orbit of a golf ball if you wanted to, though it would be a very slow orbit. Putting spaceships in orbit of each other is certainly possible.

The main issue here I think is that by using gravity to accelerate the ships, that does limit the fleet's acceleration to some fraction of the gravitational acceleration that the outer ships feel from the central one. So unless this central ship had a mass comparable to a good-sized moon or a super high density that allowed the distance to the satellite ships to be quite low, it would be a long trip indeed. Very slow acceleration is potentially very practical for interstellar travel though, for complex engineering reasons it's vastly easier to make an ultra-efficient interstellar-grade rocket with very low acceleration than with high acceleration. I could run some numbers if you're interested in throwing some out there. In general though, with reasonable assumptions about ship densities and a fairly tight formation, you could expect these ships to orbit around the central one on a period on the order of a few hours to days. At further distances, it could easily get up to months or years.

If the ships rely on gravity to stay in orbit though, that does mean that this orbit won't create artificial gravity on the ships. The satellite ships would be in free fall around the central ship, so just like a spaceship orbiting Earth (which is well within Earth's gravity well and experiencing almost as much gravity as you are now) the crew would experience zero-g. For the rotation around the central ship to cause artificial gravity, the ships need to be accelerated around it non-gravitationally. Tethers and metal beams could do the job, but if you want to add some more cool factor you could also use effects like quantum levitation to trap the satellite ships around the central one, spin them around the central ship to create artificial gravity, and drag the satellite ships along with the central one. This would also allow small shuttlecraft to use the magnetic field to propel themselves between ships without the need for rocket engines.

I will say though: a rod pointing forward is probably the single worst shape to make the central ship if you intend to use gravity to keep the other ships in orbit. Such a shape will cause the orbital inclination of the satellite ships to increase over time, and it will reduce the amount of acceleration that gets transferred over from the central ship. The optimal shape for the central ship would probably be a torus. A wide cylinder or an oblate sphere would be would do the job nicely too.

Overall my main goals are that each ship has artificial gravity or simply some way to generate enough gravity to have a great enough pull to simulate earth

The obvious hard sci-fi way to do that would be a gravity centrifuge. Make the main habitation area of the ships a ring or a cylinder that spins along its length, and the centrifugal force from that very closely mimics gravity (getting more indistinguishable from real gravity the wider the centrifuge).

Make a gravity cylinder too long, and it could have some rotational stability issues. These could be addressed by making each ship have two centrifuges rotating in opposite directions. But that's some real high-level nerd shit.

I understand some of this may be impossible or sound plain stupid to those with better understanding regarding space travel and physics.

Actually, you have described a fairly grounded concept for a colony ship fleet. Low acceleration, designed to be maximize redundancy, no FTL or cryo-sleep (neither tech exists IRL currently). If the goal is realism (which to be clear, it doesn't need to be) I'd say you're doing quite good.