Help on Tree diagram by using tikz,tikz-qtree, tikz-qtree-compat

The reason for the space is the position of the control points, +(south west:5) and +(south:5). Move them up, by reducing the distance in those polar coordinates, e.g. +(south west:2.5) and +(south:3).

One way of adding the additional arrow is to add a coordinate along the first arrow, and draw the second arrow from that. I used just trial and error to find an appropriate value for pos.

Finally, for the vertical alignment, add baseline to the options of the tikzpicture.

documentclass{book}

usepackage{tikz,tikz-qtree, tikz-qtree-compat}
usepackage{gb4e}%
begin{document}

begin{exe}
ex begin{tabular}[t]{l}%toprule%[-12pt]
begin{tikzpicture}[baseline]
label{bicycletree}
%tikzset{level distance = 25pt}
Tree[.DP [.D [.D ] [.Agr$^D$ $[+$m$+$h$+$pl$]$ ] ] [.NumP [.Num [.n$_j$ [.node(id3){$v_i$}; node(id2){$surd$BOY}; ] [.n $+m,+h$ ] ] [.Num $[+]$pl ] ] [.nP [.n$_j$ ] [.node(id1){v$_i$}; ] ] ] ]
draw[semithick,<->] (id2)..controls +(south west:2.5) and +(south:3)..(id1) coordinate [pos=0.17] (tmp);
draw [->, semithick] ([xshift=-pgflinewidth]tmp) to[bend left=40] (id3);
end{tikzpicture}
%vspace{-38pt}
end{tabular}
end{exe}

end{document}