Five warning lights, car shuddering strongly at red light; help!

This is my first post here, though I’m a longtime lurker I’m facing what might be a major issue with my 2007 Prius, 80k miles, very well cared for with no major issues or accidents. The problem started a few days ago, when I drove my car for the first time in a week, so it had been sitting for awhile. This was after a month-long cold spell in which temps were often close to 0, with lots of snow, and I keep my car outside, which means many days of scraping ice and snow off the car with it running (along with the defroster and heat). I only work part-time, and the car often sits for a few days or longer at a time without being driven.

The problem is this: I was on my way to work a few miles away and was stopped at a red light, and the car all of a sudden “shuddered” rather violently, with what sounded like the engine revving up, then switching back to silent mode, then revving up again, and so on. It freaked me out, but the light turned green and the car drove normally to my destination. Then, on my way home an hour later, a bunch of warning lights showed up: master warning, VSC, check engine, brake system, as well as hybrid system light on the center screen (car with ! through it). I pulled over, turned off the car, waited a bit, turned it back on, all the same lights were on. Drove it home with no problems. Turned it on the next day, same lights.

I decided to drive the car around for a bit to try and charge up the battery, in case that was the issue after all the cold weather and sitting around not being driven regularly. After driving it around, turning it off, then turning it back on, the brake system and VSC lights disappeared, but the rest remained. I continued driving the car for another day, and it did that same strong shuddering thing with weird engine noises while at one red light, but drove normally otherwise.

I then researched a bit more and found out how to check the health of the battery myself by holding down the display button, turning lights on and off three times, etc. The three voltage readings were all within the proper range. When I turned the car back on after completing the battery check, all of the warning lights were gone. I figured the issue had been the battery after all and that driving the car around had brought it back up to normal voltage, with the battery check resetting the system. BUT today the car did the same strong shuddering with weird engine noises while stopped at a red light. I continued driving and made it home just fine, without the issue occurring again, but this is the third time it’s done this in a week, and I’m a little freaked out by it.

Two notes:
*A little over a year ago I replaced the original battery (which died) with an Optima yellow top battery made for the Prius.
*Several weeks ago, after a major snow/ice storm, I was driving home from work when I went over either a deep pothole or hard ice formation, and the impact was really loud and scary—I actually screamed. But the car continued driving normally all the way home, and I examined the wheel area and surrounding parts with a flashlight and nothing seemed out of place. I drove the car a bunch of times in the following weeks with no issues, so this incident is probably unrelated to the problem I’m experiencing now, but I though it worthwhile to mention.

I have very little money and want to avoid taking the car to the dealer if at all possible. The dash and screen have remained warning light-free since doing the battery check, but obviously something is going on that's causing the occasional issue it's having while stopped at lights. Does anyone have any ideas as to what this problem could be, or advice for what I should do?

 

I believe they were 12.4, 12.1, 13.8, though I didn't write them down. I'll do another check now for peace of mind. Aha! This time, they were 12.1, 11.7 (switching back and forth with 11.8), and 13.8. Obviously, the 11.7/11.8 is bad, right? The first time I did the check, it was definitely above 12. My understanding is that anything less than 12 on this step means battery health is poor. If that's the case, is it likely that the shuddering and engine noises at red lights are due to battery issues?

 

I'll order/buy a battery charger today. Thanks for the info about charging it in ready mode.

I'm supposed to have new tires put on today, but I think I'll delay that appointment until I'm more certain of what the problem is. I can't afford a costly repair, so new tires will be useless on a car I can't drive. When I called the tire shop to explain the issues I was having, they said they want me to come in and have an alternator check performed. They explained why, but it was a bunch of car lingo I barely understand. Not sure if I'll go in and do this or not.

I believe this is unrelated, but the car has been sounding a single beep when I turn it off, indicating the key fob battery needs replacing. Another chore to add to the list, albeit a small one.

 

Ha, well that figures. And clearly I don't know enough about my car to have corrected him!

I just found a rather large bubble in my front driver side tire. I don't know how I didn't see it sooner, but it must have formed from that impact several weeks ago that I mentioned above. Now I'm in the position where I really need a new tire put on asap, so I'll just get this new tire set installed tomorrow or Saturday and hope that whatever the issue is with my car will not be too costly to repair.