Regarding your question, on Page 40 of "Prayers and Meditations", where it says: "Methinks He", this "He" refers to the Báb. The last paragraph on Page 40 and the continuation of it on Page 41 right down to the end of the quotation marks on Page 42, is all the Spirit of the Báb addressing Bahá'u'lláh; therefore, the words: "Thou art, in very truth, the Self-Subsisting" refers to Bahá'u'lláh, and is addressed by the Báb's Spirit to Him in the mystical sense of this prayer.
Regarding the words on Page 39 beginning with: "He it is, O my Lord," up to: "Thou didst weep continually", these are addressed by Bahá'u'lláh to the Báb.