Steering wheel shakes at all speeds over fifteen mph

I have a car I am considering buying. I got it for a day, so I am putting it through its paces. Two things I have noticed so far:

The steering wheel shakes at all speeds over fifteen mph. There is no brake pulsing not is the car pulling to either side. The shaking is very noticeable, not just a vibration. What could it be and how could I narrow down the possibilities?

There is a faint burning smell in the passenger compartment.

The car has not been driven in two to three months. Do not know if that matters.

Anything else I should check out during my test drive?

Update: I did a full test drive and inspection on the vehicle. I'm going to put the results below and I'd like to know what is a big enough deal to walk away, what should I deduct ($x from the asking price) and what is simply no big deal.

Asking price: $6,400. 151,000 miles on the car.

1) Steering wheel shakes, car pulls to the left. If I drive for awhile, I get smoke from the brake on the left front tire and it gets pretty hot. Car will not move forward when in drive without pressing on the pedal. My diagnosis: Frozen caliper.

2) 3 of 4 struts have torn boots. Struts look otherwise OK.

3) Silver coating on wheels crackling/rusting off

4) Low tread on one front tire

5) Leather torn on both front seats