Finite lattice representation problem checking

Answer to Question 1:

All other lattices of size at most 7 are known to be representable as the congruence lattice of a finite algebra. See my thesis and this MO question.

Answer to Question 2: The same lattice that answers question 1.

However, there may be other 7-element lattices that are not known to occur as intervals in subgroup lattices of finite groups.

It is know that every lattice of size at most 6 is "group representable" in the above sense. See Watatani (1996) MR1409040 and Aschbacher (2008) MR2393428.