Your second questions concerns the gaps between semi primes. It turns out that we can find infinitely many solutions to $$1\leq qp-rs\leq a$$ for all $a\geq 26$, and that under the Elliott-Halberstam Conjecture, we can take $a\geq 6$
In their work, Daniel A. Goldston, Sidney W. Graham, Janos Pintz and Cem Y. Yıldırım prove that if $q_n$ is the $n^{th}$ almost prime, then $$\liminf_{n\rightarrow \infty} q_{n+1}-q_n \leq 26.$$