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This is a Praying Mantis from the Genus Empusa.
(The Walking Stick Phobaeticus is from Asia so this has nothing to do with it)
A male Phasmid of the Tribe Necrosciini.
This looks a close relative to the Genus Lamponius.
Nice insect! But this is a katydid species and not Phyllium sp.
Cockroaches lay their eggs in ootheca (egg mass). This is a pupa.
Not a sand cockroach, they have a round, brownish body, the head is located under the pronotum and they have very small eyes. Also the form of the antenna is different from that of cockroaches. I think this is a Crustacea.