Though I am relatively new to LaTeX but breaking your query into following
- No bold numbers
- Indentation alignment
As far as the bold part is concerned I feel you need to break the label into 2 parts--the first part is the counter and the second part is the actual label text--the counter is incrementing the numbers, but the text remains User defined
\newcounter{notes}
\newenvironment{Notes}
{\begin{list}{\textsc{Note} \arabic{notes}.}%
{\setlength\labelsep{10pt}%
\setlength\itemindent{10pt}%
\setlength\leftmargin{0pt}%
\setlength\labelwidth{0pt}%
\usecounter{notes}}}%
{\end{list}}
As you can see above the \textsc{Note} is separated from the counter \arabic{notes}.
Putting this list to use would be as follows
\begin{Notes}
\item This is the text of the first note item.
Some more text for the first note item.
\item This is the text of the second note item.
Some more text for the second note item.
\end{Notes}
and would yield the following output

Now if I was to inverse the counter to precede the text label as below
\newcounter{notes}
\newenvironment{Notes}
{\begin{list}\arabic{notes}.{\textsc{Note}}%
{\setlength\labelsep{10pt}%
\setlength\itemindent{10pt}%
\setlength\leftmargin{0pt}%
\setlength\labelwidth{0pt}%
\usecounter{notes}}}%
{\end{list}}
and then use it in the list environment would yield
\documentclass{article}
\usepackage{enumitem}
\usepackage{environ}
\begin{document}
\newcounter{notes}
\newenvironment{Notes}
{\begin{list}{\arabic{notes}.\textsc{Note}}%
{\setlength\labelsep{10pt}%
\setlength\itemindent{10pt}%
\setlength\leftmargin{0pt}%
\setlength\labelwidth{0pt}%
\usecounter{notes}}}%
{\end{list}}
\begin{Notes}
\item This is the text of the first note item.
Some more text for the first note item.
\item This is the text of the second note item.
Some more text for the second note item.
\end{Notes}
\end{document}

You can see the change in the counter position and it is not bold
I have not removed the period after the counter for clarity
Now if I bold the text of the label which follows the counter and remove the period
{\begin{list}{\arabic{notes}\textsc{\textbf{ Note}}}
this yields

This ends part 1 of the exercise
The other part is to carry out indentation alignment available at https://tex.stackexchange.com/a/130099/197451
\documentclass{article}
\usepackage{enumitem}
\usepackage{environ}
\newlength\widest
\makeatletter
\NewEnviron{ldescription}{%
\vbox{%
\global\setlength\widest{0pt}%
\def\item[##1]{%
\settowidth\@tempdima{\textbf{##1}}%
\ifdim\@tempdima>\widest\global\setlength\widest{\@tempdima}\fi%
}%
\setbox0=\hbox{\BODY}%
}
\begin{description}[
leftmargin=\dimexpr\widest+0.5em\relax,
labelindent=0pt,
labelwidth=\widest]
\BODY
\end{description}%
}
\makeatother
\begin{document}
\begin{ldescription}
\item[Short] text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text
\item[A really really long label] text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text
\end{ldescription}
\begin{ldescription}
\item[Short] text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text
\item[A medium label] text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text
\end{ldescription}
\end{document}
which yields the following indentation

This ends part 2 of the exercise
A combination of the ideas generated above in part 1 and part 2 should suffice to produce a counter(no bold) as well as the User desired indentation
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