1994 Lexus SC 400 Two things

I just bought this car recently, and it was in pristine condition. No cracks in the leather and everything under the hood is well maintained and clean. When I drive the car at about 42-48 mph steadily, it tends to sputter a little bit while holding that speed. You can feel it in the gas pedal. It requires premium fuel, which I put into it, so I'm pretty sure that isn't it. I do not know when or if the timing belt had been changed or a tune up had been done, so I wonder if this could be an issue.

Then, last night my battery light came on and barely made it home before the battery died. Something is not allowing the battery to charge. I am familiar with a common problem this model has with the steering pump leaking onto the altenator, but there are no leaks visible.

Any ideas?