1. From reading the other translations, it becomes clear that there is some differences of opinion as to what it is that actually prospers. NIV, NKJ, and KJV make "all that he does" the subject. NRS changes the singular nouns of the Hebrew text into plurals and makes the person(s) who is(are) "like a tree planted by streams of water" the subject of the verb 'prospers.' ESV, RSV and NASB retain the singular but agree otherwise with the NRS regarding the subject. In a similar vein, J. Goldingay translates this as "he makes everything that he does thrive" (Psalms. Vol. 1: Psalms 1-1., 79n.c.). The syntax of the Hebrew sentence is ambiguouus; it is possible for either the man or the "everything he does," or the tree to be the subject of the verb "prospers." In doing as he did, however, Goldingay shifts the efficacy to the activity of the man, when the thrust of the psalm is that such efficacy—even as it is evidenced in the maturing of the fruits on the tree and the "lushing" of its leaves—is due to being planted by the streams of water.
2. John Goldingay, Psalms. Vol. 1, Psalms 1-41. (Baker Commentary on the Old Testament; Grand Rapids: Baker, 2006), 42.