Kia Rio 5S - 2011 - squeals when cold, feels like it's going to stall when warm.

The two issues may be unrelated, but I've taken this car to my own mechanic, who
did a tune up and replaced the spark plugs, who now says I need a priest. The used
car dealership who told me she needs (another?) tune up. And finally an actual Kia
dealership who told me nothing is wrong, she starts and drives fine.
When I start her in the morning she starts to squeal after about 10 seconds after I
start her, and forget about moving! She has no power steering and the battery light
comes on when I do try to move the steering wheel. After a few minutes I fight the
steering and go about my drive to work, and she continues to squeal, sorry
neighbours! The power steering kicks in and the squealing usually stops after a
couple blocks, but will sometimes start squealing again when I have to stop at a light.
After about 20 minutes of driving, she's all warmed up and quiets down. Enter part
two of her issues. Now that she's warmed up she'll start to chug. This started after I
had the spark plugs changed, and yes the mechanic has checked them out to make
sure everything was done correctly. Basically when I have to stop, at a light, stop
sign, drive thru, this car will do like a chug or a shudder and feel like she's about to
stall out. Sometimes it's worse and happens a few times at a light, sometimes it's a
light shudder. Sometimes it doesn't happen at all. Her check engine light has come
on a couple times, the code is a "random cylinder misfire," but that hasn't happened
in a few months and of course the code isn't there for the dealership to read as the
other place cleared the code. I've replaced the battery a few months ago too as it
died on me. She's at 120,000 kms. I don't trust this car to get me anywhere but to
and from work, and even then I feel sketchy, but yet not even the Kia Dealership
seems to be able to tell me what's wrong with her. Any ideas?