Not only 'again,' but 'entirely afresh,' as from a new source of life and point of departure; translated in Luke 1.3, 'from the origin.' It is a new source and beginning of life.
I have hesitated a moment whether 'so' referred to the kind of love that gives 'eternal life,' which is mentioned in verse 15, and is the great subject of John, in contrast with all earthly blessings and favour. The sense then would thus be, that he has loved men in view of eternal life, 'so that' he has given, &c. (See 'so,' Acts 14. 1.) When followed by 'that,' the regular force of the Greek is, 'so much that.'
Eis, as in ver. 36; chs. 4.39; 6.29,35,40.
Elenko: to show the true character of anything, so as to convict, and hence reprove by showing a man's fault. It is used in chs. 8.46, 'convinces;' 16.8, 'bring demonstration;' Eph. 5.11,13, 'reprove' and 'expose.'
Or 'believes not on.' It is the obedience of submission to his person, not practical obedience to his commands, whatever proof this may be of the other; but it is not exactly the same thing as believing on him as an object revealed in grace: see Note, Heb. 3.18.