Two questions for $p$-group

Two questions for $p$-group

I would like to ask two questions. Kindly help me in this regard:
(1) In Finite p-group with a cyclic frattini subgroup., user28083 has
given finite $p$-group with cyclic frattini subgroup. I need the reference
of this.
(2) Suppose $G$ is group of order either $p^4$ or $p^5$ ($p$ a prime) such
that all subgroups of order $p$ of non cyclic frattini subgroup are normal
in $G$. What are the choice for $G$? I don't want to use the
classification of these. Could you kindly provide a simple argument for
that?
with regards
Vipul