How to add a "qed square" at the end of a definition?

Question

I'm using the acmart documentclass for a conference paper submission. I've provided a simple example (code below) which currently renders to the following output:

Questions:

1. How can I change the "definition" environment so that the text "Definition" looks the same as the text "Theorem" (remove the italicization and the Font seems to be different as well)?
2. How I add a new "Remark" environment which displays the same as the ones (theorem, lemma, corollary, ...) which are already present?
3. How can I add a "qed square" of the same size to the end of any of these environments (even when they have no "proof")?

Code:

\documentclass[acmtog,anonymous,review]{acmart}
\usepackage{graphicx}
\AtEndPreamble{%
\theoremstyle{acmtheorem}
\newtheorem{remark}[theorem]{Remark}}
\begin{document}
\section{}
\begin{theorem}
    A theorem.
    \begin{proof}
    \end{proof}
\end{theorem}
\begin{definition}
    A definition.
    \begin{flushright}
        $\square$
    \end{flushright}
\end{definition}
\begin{remark}
    A remark.
    \begin{flushright}
        $\square$
    \end{flushright}
\end{remark}
\end{document}

Answer 1

If you're submitting to a conference, you shouldn't try to modify their standard. Anyway, here's how you can do.

\documentclass[acmtog,anonymous,review]{acmart}
\AtEndPreamble{%
  \theoremstyle{acmplain}%
  % note to copy editors: remove the following
  % two lines if standard ACM style is preferred
  \let\definition\relax\let\enddefinition\relax
  \newtheorem{definition}[theorem]{Definition}%
  % end note to copy editors
  \newtheorem{remark}[theorem]{Remark}%
  \AtBeginEnvironment{definition}{\pushQED{\qed}}%
  \AtEndEnvironment{definition}{\popQED}%
  \AtBeginEnvironment{remark}{\pushQED{\qed}}%
  \AtEndEnvironment{remark}{\popQED}%
}
\begin{document}
\section{Test}
\begin{theorem}
A theorem.
\end{theorem}
\begin{proof}
And its proof.
\end{proof}
\begin{definition}
A definition.
\end{definition}
\begin{remark}
A remark.
\end{remark}
\end{document}

Notes.

1. The standard theorem style is acmplain.
2. A proof doesn't belong to the theorem.

Answer 2

I understood your question to mean that you want theorems, definitions, and remarks to all have of the same styling. In that case, I'll answer your questions out of order:

2. How I add a new "Remark" environment which displays the same as the ones (theorem, lemma, corollary, ...) which are already present?

Edit: based on your comment, I believe you want all three environments to have small caps for the headers and non-italicized font for the main text.

Firstly, you'll need to define a new theorem style, since neither of acmart's predefined theorem styles suit your needs. The acmart class documentation provides the source code for the definition of the acmplain theorem style (on page 110, I believe), so you can copy-paste that definition into your own code and modify it as you see fit. Then you can use \theoremstyle{your-style-name} to set the styling of your custom theorem environments.

1. How can I change the "definition" environment so that the text "Definition" looks the same as the text "Theorem" (remove the italicization and the Font seems to be different as well)?

Since there's no straightforward way to modify the definition of a theorem environment, you'll have to define the styling of definition (and theorem) yourself. You have two options:

1. Define your own definition and theorem environments with different names so that they don't clash with the existing environments. I recommend this option since it's the most straightforward, and it doesn't overwrite the existing definitions (in case that might cause issues with your submission).
2. Suppress the existing environment definitions with the class option acmthm=false. Then you can define your own definition and theorem environment without clashing with any existing environments. Note that this suppresses all theorem environments defined by acmart, including theorem, proposition, definition, example, etc. Thus, if you choose this option, you'll have to define all the other environments yourself as necessary.

3. How can I add a "qed square" of the same size to the end of any of these environments (even when they have no "proof")?

I recommend using the thmtools package for your custom environment definitions, as this makes setting the QED symbol very easy. This solution is suggested in the post linked by @barbara-beeton in the comments, but it's the third one down. Refer to the thmtools package documentation for more details.

New and improved MWE (with custom environments under different names):

\documentclass[acmtog, anonymous, review]{acmart}
\usepackage{thmtools}
\makeatletter
\AtEndPreamble{
    % Modified from definition of acmplain
    % acmart documentation, page 110
    % https://mirror.las.iastate.edu/tex-archive/macros/latex/contrib/acmart/acmart.pdf
    \newtheoremstyle{mystyle}%
        {.5\baselineskip@plus.2\baselineskip
            @minus.2\baselineskip}% space above
        {.5\baselineskip@plus.2\baselineskip
            @minus.2\baselineskip}% space below
        {\normalfont}% body font
        {@acmplainindent}% indent amount
        {\scshape}% head font
        {.}% punctuation after head
        {.5em}% spacing after head
        {\thmname{#1}\thmnumber{ #2}\thmnote{ {@acmplainnotefont(#3)}}}% head spec
\theoremstyle{mystyle}
\declaretheorem[name=Theorem, parent=section]{thm}
\declaretheorem[name=Definition, qed=$\square$, sibling=thm]{defn}
\declaretheorem[name=Remark, qed=$\square$, sibling=thm]{remark}

}
\makeatother
\begin{document}
\section{}
\begin{thm}
    A theorem.
    \begin{proof}
    \end{proof}
\end{thm}
\begin{defn}
    A definition.
\end{defn}
\begin{remark}
    A remark.
\end{remark}
\end{document}