Erdos-Kac law state a typical number of magnitude $n$ has $\log\log n$ prime factors.

What is magnitude and distribution of largest prime factor of typical magnitude $n$ natural number?

What is magnitude and distribution of largest and second largest prime factor of typical magnitude $n$ natural number given than there is a prime factor $p|n$ of size $n^{0.25\pm\epsilon}$?

Assume $\epsilon\in(0,0.25)$ is fixed.

I am also interested in 1. and 2. for square-free scenario.