Problem With Transmission/alternator?

Hi there, first time poster here. I'm taking my vehicle to a tranny shop next week and hoping to gather some more information beforehand if possible.

I'm having two problems with my 2002 Focus w/ an auto transmission. One is that during acceleration, seemingly in any gear, the transmission will "skip" and downshift for a couple seconds, then "knock" back into the appropriate gear. This leads me to believe there is an issue with the transmission, hence my appointment with the tranny shop to scan the thing and make sure all codes are correct. The second issue is that the headlights and radio have begun flickering and dimming. This makes me think the alternator is at fault. Often, but not always, these two issues will happen at the same time; the transmission downshifts and the radio & headlights flicker, then they correct themselves almost immediately.

I'll add that 10 months ago I had a new radio installed; no amp or anything, just a head unit. Other than that this vehicle has had no major issues or repairs in its 12-year, 85,000 kilometer lifespan.

Is the alternator and transmission linked in some way? Could this be a battery issue? Fuses? Or two separate issues altogether? Are these issues a cause for concern?

I'd appreciate the insight that any of you have into the innerworkings of this vehicle, whether you've experienced similar issues or simply know more about it than I do and are willing to share.

Thanks in advance,

Alex