Amsart Title Whitespace Problem

another method for countering the space above the title is to nullify the \topskip applied above the title. this is used elsewhere, so the value isn't changed, but a reversing \vspace* is added after it:

\usepackage{etoolbox}
\makeatletter
\patchcmd{\@maketitle}{\global\topskip42\p@\relax}
  {\global\topskip42\p@\relax \vspace*{-38pt}}
  {}{}
\makeatother

it's easy to change this value if you decide you want something slightly different.

the code should be put in your preamble. i suggest at the very top, immediately following the \documentclass line.

I don't find the space is excessive. However, here's an easy way for adjusting the spacing, act where indicated after experimenting with the values.

I removed your hack for sharing the counter between equations and theorems and alike environments to a better one.

Remove the showframe option to geometry for the production version.

\documentclass[11pt,reqno]{amsart}

%-------Packages-----------------------
\usepackage{amssymb,amsfonts}
\usepackage[all,arc]{xy}
\usepackage{enumerate}
\usepackage{mathrsfs}
\usepackage[a4paper, top=2.8cm, left=2cm, right=2cm, bottom=2cm,showframe]{geometry}
\usepackage{wrapfig}
\usepackage{tikz}
\usepgflibrary{arrows} 
\usepgflibrary[arrows] 
\usetikzlibrary{arrows}
\usetikzlibrary[arrows]
\usetikzlibrary{automata} 
\usetikzlibrary[automata] 
\usetikzlibrary{positioning}
\usepackage{framed}
\usepackage{multicol}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{etoolbox}
\usepackage{lipsum}      %used for this example
\usepackage{hyperref}


%--------Theorem Environments----------
\numberwithin{equation}{section}
\newtheorem{thm}[equation]{Theorem}
\newtheorem{cor}[equation]{Corollary}
\newtheorem{prop}[equation]{Proposition}
\newtheorem{lem}[equation]{Lemma}
\newtheorem{conj}[equation]{Conjecture}
\newtheorem{quest}[equation]{Question}

\theoremstyle{definition}
\newtheorem{defn}[equation]{Definition}
\newtheorem{defns}[equation]{Definitions}
\newtheorem{con}[equation]{Construction}
\newtheorem{exmp}[equation]{Example}
\newtheorem{exmps}[equation]{Examples}
\newtheorem{notn}[equation]{Notation}
\newtheorem{notns}[equation]{Notations}
\newtheorem{addm}[equation]{Addendum}
\newtheorem{exer}[equation]{Exercise}

\theoremstyle{remark}
\newtheorem{rem}[equation]{Remark}
\newtheorem{rems}[equation]{Remarks}
\newtheorem{warn}[equation]{Warning}
\newtheorem{sch}[equation]{Scholium}

\makeatletter
\patchcmd{\@settitle}
  {\begin{center}}
  {\vspace*{-3\baselineskip}\begin{center}}% <--- adjust the dimension
  {}{}
\patchcmd{\@setauthors}
  {30\p@}
  {20\p@}% <--- adjust the dimension
  {}{}
\patchcmd{\@setauthors}
  {\endtrivlist}
  {\endtrivlist\vspace{-2\baselineskip}}% <--- adjust the dimension
  {}{}
\makeatother

\bibliographystyle{plain}

%--------Info----------------------------
\title{Title}
\author{Author}
%----------------------------------------

\begin{document}

\maketitle

\section{A title}

\lipsum[1]

\begin{thm}
A theorem statement with an equation
\begin{equation}
x=x
\end{equation}
and some text after it.
\end{thm}

\lipsum[2]

\begin{rem}
A remark.
\end{rem}

\lipsum

\end{document}

The \vspace{-1cm} command inside \author is of no use. Just type \space*{-1.2cm}just before \maketitle.

Alternatively you might want to take a look at the titling package, which provides tools to customise the \maketitle command in a clean way.

Unrelated: the hyperref package should be loaded as the last one, with very few exceptions.

\documentclass[11pt,reqno]{amsart}

 %-------Packages-----------------------
\usepackage{amssymb,amsfonts}
\usepackage[all,arc]{xy}
\usepackage{enumerate}
\usepackage{mathrsfs}
\usepackage[a4paper, top=2.8cm, left=2cm, right=2cm, bottom=2cm, showframe]{geometry}
\usepackage{wrapfig}
\usepackage{tikz}
\usepgflibrary{arrows}
\usepgflibrary[arrows]
\usetikzlibrary{arrows}
\usetikzlibrary[arrows]
\usetikzlibrary{automata}
\usetikzlibrary[automata]
\usetikzlibrary{positioning}
\usepackage{framed}
\usepackage{multicol}
\usepackage{caption}
\usepackage{subcaption}
\usepackage[english]{babel} %used for this example
\usepackage{blindtext} %used for this example
\usepackage{hyperref}


%--------Theorem Environments----------
\newtheorem{thm}{Theorem}[section]
\newtheorem{cor}[thm]{Corollary}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{conj}[thm]{Conjecture}
\newtheorem{quest}[thm]{Question}

\theoremstyle{definition}
\newtheorem{defn}[thm]{Definition}
\newtheorem{defns}[thm]{Definitions}
\newtheorem{con}[thm]{Construction}
\newtheorem{exmp}[thm]{Example}
\newtheorem{exmps}[thm]{Examples}
\newtheorem{notn}[thm]{Notation}
\newtheorem{notns}[thm]{Notations}
\newtheorem{addm}[thm]{Addendum}
\newtheorem{exer}[thm]{Exercise}

\theoremstyle{remark}
\newtheorem{rem}[thm]{Remark}
\newtheorem{rems}[thm]{Remarks}
\newtheorem{warn}[thm]{Warning}
\newtheorem{sch}[thm]{Scholium}

\makeatletter
\let\c@equation\c@thm
\makeatother
\numberwithin{equation}{section}

\bibliographystyle{plain}

%--------Info----------------------------
\title{Title}
\author{\vspace{-0.5cm}Author\vspace{-1cm}}
%----------------------------------------

\begin{document}

\vspace*{-1.2cm}
\maketitle
\Blinddocument

\end{document}