A Baptized lay person…can Bless. He is a Christian. Called in fact to bless and be a blessing…(not commenting directly on the examples…but in general …of course only in proper ways)
The blessing here of course is different than that of the ministerial Priesthood.
And one can not “Bless Sacramentals”…like medals etc…
But for sure pray…“ask the blessing of God” etc…bless your children etc…
The sign of the cross has been used since the very early days… Early Christians would use it all the time…
in the early Church it was made on the fore head with a + (and still is at the Gospel…and one can of course always use do it this way too personally outside formal liturgical times…i do…)
“let us then not be ashamed to confess the Crucified. Be the cross our seal, made with boldness by our fingers on our brow and in every thing; over the bread we eat and the cups we drink, in our comings and in goings; before our sleep, when we lie down and when we awake; when we are travelling, and when we are at rest”. St. Cyril of Jerusalem
In all our travels and movements, in all our coming in and going out, in putting on our shoes, at the bath, at the table, in lighting our candles, in lying down, in sitting down, whatever employment occupies us, we mark our forehead with the sign of the cross."
–Tertullian
“Making the sign of the cross – as we will do during the blessing – means saying a visible and public “yes” to the One who died and rose for us, to God who in the humility and weakness of His love is the Almightly, stronger than all the power and intelligence of the world.”
-Pope Benedict XVI
Angelus
September 11, 2005
he also talks about it when he was Cardinal in the Spirit of the Liturgy…as a renewal of baptism…as a shield…etc…and about blessing…go read that chapter!