Move grounds to subpanel when I moved 8 single pole breakers to same subpanel

1) Replacing the subpanel is a very good idea -- FPE Stab-Loks are absolute junk that have a well-known propensity for failing to do their job when called upon, and also are susceptible to faults in the busbar-to-breaker contacts (high resistance/overheating) that are documented to cause the symptoms you're seeing -- this phenomenon can develop into a full-fledged electrical fire!

If a complete replacement of the subpanel is impractical for whatever reason, there is also the option of gutting the box and using one of the Eaton CH retrofit kits to replace the innards. Since your box is a mere, oh, 7" wide by 11" tall, this requires an Eaton RWCH6L125N retrofit interior, the matching cover (a CRWCH6ML of the appropriate size), and the appropriate Eaton CH breakers (it looks like you can use a CH220 and a CH250 along with a pair of CHT1515s, but I'd need to know more about what this subpanel feeds in order to specify for certain).

2) You will need to run a ground wire from the subpanel to the main panel, and separate the ground and neutral bars in the subpanel; however, you do not need a GEC + grounding electrode for a subpanel in the same building as the main panel, as such an installation falls under NEC 215.6:

215.6 Feeder Equipment Grounding Conductor. Where a feeder supplies branch circuits in which equipment grounding conductors are required, the feeder shall include or provide an equipment grounding conductor in accordance with the provisions of 250.134, to which the equipment grounding conductors of the branch circuits shall be connected. Where the feeder supplies a separate building or structure, the requirements of 250.32(B) shall apply.

Given that you are feeding two separate structures, I see two problems with your setup so far:

1. The house is relying on the grounding electrodes at the pole, which improperly multiplexes the equipment grounding conductor from the panel to the house with the grounding electrode conductor for the house. This is easily fixed by driving and connecting a ground rod or grounding to an underground metal water pipe at the house, using #4 bare copper or equivalent Bare Armored Ground cable if you prefer.
2. The neutral and ground need to be separated at the garage subpanel, and a ground wire needs to be run from the main panel . This requires pulling the bonding screw or strap from the panel (it'll be green on more modern ones), installing an extra ground bar to the panel (ground bar kits are available for all panel types in current production, just ask your local electrical supply house; if you can't find one, post here with information/photos of the panel and we can help), and moving the ground wire connections over to the new ground bar, as well as pulling a #8 (or larger) bare or green THHN/THWN through the existing conduit to serve as a new ground wire -- it will connect to the combination ground/neutral bar in the main panel and the new ground bar in the garage panel. (You have plenty of room in the conduit, by the way -- roughly 680mm^2 used to 1660mm^2 available by the 40% fill rule for more than 2 conductors, and the new wire puts you at roughly 710mm^2 used.)