From the texts of the wondrous, heavenly Scriptures they should memorize phrases and passages bearing on various instances, so that in the course of their speech they may recite divine verses whenever the occasion demandeth it, inasmuch as these holy verses are the most potent elixir, the greatest and mightiest talisman.
(Bahá’u’lláh, Tablets of Bahá’u’lláh, p. 200)
I hope thou wilt memorize all the poetry of the Blessed Perfection and chant with wonderful melody in the assemblages and gatherings … and then this Divine Song will rise from those lands and reach the ABHA Kingdom in utmost joy and happiness.
(‘Abdu’l-Bahá, Tablets of ‘Abdu’l-Bahá v1, p. 212)
If a believer finds it difficult to memorize, he may be encouraged to make for his own use a selection of extracts, however brief, which he could reread and enjoy at his own leisure, to satisfy his inner soul.
(NSA USA - Developing Distinctive Bahá’í Communities)
It is also highly praiseworthy to memorize the Tablets, divine verses and sacred traditions.
(‘Abdu’l-Bahá, The Compilation of Compilations vol. I, p. 195)
Regarding the questions you asked him: there is no objection to children who are as yet unable to memorize a whole prayer learning certain sentences only.