Arrows inside a commutative diagram using tikzcd
You can shorten
a Rightarrow
as you like.
For the triangle, you can name the label and draw an arrow to it.
\documentclass[12pt,reqno,a4paper]{amsart}
\usepackage{tikz-cd}
\tikzcdset{row sep/normal=50pt, column sep/normal=50pt}
\begin{document}
\begin{tikzcd}
A\arrow[d, "p"']\arrow[Rightarrow, shorten >=25pt, shorten <=25pt, dr]\arrow[r, "q"] & B\arrow[d, "r"]\\
C\arrow[r, "s", swap] & D
\end{tikzcd}
\begin{tikzcd}
A\arrow[d, "p"']\arrow[r, "q"] & B\arrow[d, "r"]\\
C\arrow[r, "s", swap]\arrow[Rightarrow, shorten >=25pt, shorten <=25pt, ur] & D
\end{tikzcd}
\begin{tikzcd}
A\arrow[d, "p"']\arrow[rd, "q"{name=M}] \\
B\arrow[r, "r", swap]\arrow[Rightarrow, shorten >=10pt, shorten <=10pt, to=M] & C
\end{tikzcd}
\end{document}
Why not simply this, to specify the diagram commutes? Unrelated: I took the liberty to simplify your code, in particular removing unnecessary packages (already loaded by another package).
\documentclass[12pt,reqno,a4paper]{amsart}
\usepackage{extsizes}
\usepackage{blindtext}
\textheight 9.3in \textwidth 6.5in
\calclayout
\usepackage{mathtools}
\usepackage{amsthm,amssymb}
\usepackage{hyperref}
\usepackage{mathrsfs}
\usepackage[all]{xy}
\usepackage[normalem]{ulem}
\usepackage{tikz-cd}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\pagestyle{myheadings}
\begin{document}
\begin{tikzcd}[row sep = large, column sep = large]
A \arrow[d, "p"'] \arrow[r, "q"] & B \arrow[d, "r"] \\
C \arrow[ur, phantom, "\scalebox{1.5}{$\circlearrowleft$}" description]\arrow[r, "s"] & D
\end{tikzcd}
\end{document}
You can use a phantom arrow, with the label in the middle via description
and sloped
.
\documentclass[12pt,reqno,a4paper]{amsart}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}[sep=huge]
A \arrow[dr,phantom,"\to" description, sloped]
\arrow[d, "p"'] \arrow[r, "q"] & B \arrow[d, "r"] \\
C \arrow[r, "s"] & D
\end{tikzcd}
\end{document}