Yes you would need an "N" router/access point for your laptop with an N NIC to be able to run in N mode. If your laptop is just associated with a G or B access point or router..it will only run in those modes.
Yes most peoples experience with N routers/access points have shown that the increase in range/distance is substantially better. Throughput is often quite a bit better...although this varies greatly. It's usually at least higher throughput than G. Some people get a little more, some people get a lot more. With with all things wireless....your experience may vary.
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