Six months with no air added to the tires would see a significant drop in tire pressure I would think and that could definitely lead to a vagueness about the steering. That said, the tip over could be a contributary factor too. of course.
Yes, a chain that loose could introduce jerkiness when you twist the throttle (as it takes up the slack), but it’s easy to adjust. Usually about an inch (total) of chain movement is “within spec.” for most bikes.
If I were you, I’d ride a few other bikes in the meantime and if you’re still interested in that SV650, go back, inflate the tires to the correct pressures and try it again (comparing it to the ride of the other bikes).
If you still have any doubts whatsoever, then don’t buy it.
Although I haven’t ridden one, SV650s seem to be well loved by both the experienced and not so experienced riders, so you’re on the right track.