Why even bother with sampling profilers in Python? You can do full function traces for literally all of your code in production at ~1-10% overhead with efficient instrumentation.
That depends on the code you're profiling. Even good line profilers can add 2-5x overhead on programs not optimized for them, and you're in a bit of a pickle because the programs least optimized for line profiling are those which are already "optimized" (fast results for a given task when written in Python).
It does not, those are just very inefficient tracing profilers. You can literally trace C programs in 10-30% overhead. For Python you should only accept low single-digit overhead on average with 10% overhead only in degenerate cases with large numbers of tiny functions [1]. Anything more means your tracer is inefficient.