For (1), one method might be to use linebreaks (\n) in the ylabel and title keywords using Plots:
using Plots, Plots.PlotMeasures
gr(size=(1200,800), xtickfontsize=13, ytickfontsize=13, xguidefontsize=16, yguidefontsize=20, legendfontsize=12, titlefontsize=20, dpi=100)
offsetlines = plot(rand(10), ylabel="top line \n \n \n bottom line", title="top line \n \n \n bottom line", margin=10mm)
savefig(offsetlines, "offsetlines.png")
which produces the following:
