Practical hard 3-sat instances
do we know for which $n_0$ these assumptions "kick in" in the case of $3-SAT$? Can we generate, or at least be confident of the existence of a relatively small formula ($&lt; 200$), such that every algorithm requires $\sim2^{200}$ operations? 


$3-SAT$ is known to be solvable in time $O(1.321^n)$. Therefore, there is no instance that would force a $\Omega(2^n)$ run time. SETH does not hold for $k-SAT$ for any bounded $k$; it is only expected to hold for general Satsifiability (with no limit on clause size). We don't really know what asymptotic runtime to expect for $k$-SAT for any $k$ (other than something exponential).

Also, for any $SAT$ formula, there is an algorithm solving it in $O(n)$ time. You could never hope to find a single example hard for all algorithms.

One way to generate hard SAT instances is to reduce from Integer Factorization.