I don't now if quadruple bonds can be made with chemfig but the curved bonds are no problem.
With the tikz library "pathmorphing" and the following code
\chemfig{A-[,3,,,decorate,decoration=snake]B}
you get this:
Other shapes can be made with nodes.
Try this code for example
\chemfig{@{a}A-[,,,,draw=none]@{b}B}
\chemmove{\draw[-](a)..controls +(45:7mm) and +(225:7mm)..(b);}
to get the following:
Explanation:
225:7mm
225 is the angle and 7mm is the amplitude of the bond. Our bond enters B in an angle of 225° and the curve has it's minimum at y=-7mm.
Demo code:
\documentclass[a4paper,11pt]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage{chemfig}
\usepackage[T1]{fontenc}
\usepackage{chemfig}
\usetikzlibrary{decorations.pathmorphing}
\begin{document}
\schemestart
\chemfig{A-[,3,,,decorate,decoration=snake]B}
\schemestop
\par
\schemestart
\chemfig{@{a}A-[,,,,draw=none]@{b}B}
\chemmove{\draw[-](a)..controls +(45:7mm) and +(225:7mm)..(b);}
\schemestop
\end{document}
Please make sure to run the compilation twice to make the curved bonds appear!
chemformula
myself: multiple bonds are easy enough and I think banana ones are quite doable once I remember the correct TikZ code.)