1. Grids

Grids can be made using LaTeX.

grid_1cm_squares

png pdf tex

grid_dots

png pdf tex

grids_10by10cm

png pdf tex

grids_16by25cm

png pdf tex

1.1. 1cm squares

A grid of 1cm squares can be made with the gridpapers package.
See the gridpapers package docs at:
https://mirror.cse.unsw.edu.au/pub/CTAN/macros/LaTeX/contrib/gridpapers/gridpapers.pdf

% 17 by 25 1 cm squares
\documentclass{article}
\usepackage[pattern=std,patternsize=10mm,colorset=std,majorcolor=black,minorcolor=lightgray,textarea,geometry={a4paper, portrait, hmargin=2cm, vmargin=2.35cm}]{gridpapers}

\begin{document}
\thispagestyle{empty}
\begin{tikzpicture}
~
\end{tikzpicture}
\end{document}

1.1.1. gridpapers

This line of LaTeX code

\usepackage[pattern=std,patternsize=10mm,colorset=std, majorcolor=black,minorcolor=lightgray,textarea, geometry={a4paper, portrait, hmargin=2cm, vmargin=2.35cm}]{gridpapers}

loads the gridpapers package with the following options:

patternsize=10mm: sets the size of the pattern to 10mm.
majorcolor=black: sets the color of the major grid lines to black (outer border lines).
minorcolor=lightgray: sets the color of the minor grid lines to light gray.

1.1.2. geometry

geometry={a4paper, portrait, hmargin=2cm, vmargin=2.35cm}: sets the page geometry to A4 paper size with portrait orientation and 2cm margins on the left and right sides and 2.35cm margins on the top and bottom sides.

1.2. TikZ

The following LaTeX uses draw or filldraw from the TikZ package.

See: https://en.wikibooks.org/wiki/LaTeX/PGF/TikZ

1.3. dots at 1cm

A grid of dots 1cm apart can be made by drawing small circles.

% 16 by 25 dots 1cm apart
\documentclass{article}
\usepackage[a4paper, portrait, hmargin=2cm, vmargin=2cm]{geometry}
\usepackage{tikz}
\thispagestyle{empty}

\begin{document}
\begin{tikzpicture}
  \foreach \x in {0,...,16} {
    \foreach \y in {0,...,25} {
      \filldraw[black] (\x,\y) circle (.5pt);
    }
  }
\end{tikzpicture}
\end{document}

The command \filldraw[black] (\x,\y) circle (.5pt) draws circles with a radius of 0.5pt. The command fills the circle with black color and draws its border.

See: https://LaTeXdraw.com/tikz-shapes-circle/

1.4. graph paper grids 10 by 10cm

The LaTeX code below is for 10 by 10 cm graph paper with small squares every 2mm, large squares every 1cm.

\documentclass[border = 3mm]{standalone}
\usepackage{tikz}

\def\width{10cm}
\def\height{10cm}
\thispagestyle{empty}

\begin{document}
\begin{tikzpicture}
  \draw[step=2mm, line width=0.1mm, black!30!white] (0,0) grid (\width,\height);
  \draw[step=1cm, line width=0.2mm, black] (0,0) grid (\width,\height);
  \draw[step=5cm, line width=0.35mm, black] (0,0) grid (\width,\height);
\end{tikzpicture}
\end{document}

1.5. graph paper grids 16 by 25cm

The LaTeX code below is for A4 16 by 25cm graph paper with small squares every 2mm, large squares every 1cm.

% Graph paper A4 21 x 29.7 cm
\documentclass{article}
\usepackage[a4paper, portrait, hmargin=2cm, vmargin=2cm]{geometry}
\usepackage{tikz}
\def\width{16cm}
\def\height{25cm}
\thispagestyle{empty}

\begin{document}
\begin{center}
\begin{tikzpicture}
  \draw[step=2mm, line width=0.1mm, black!30!white] (0,0) grid (\width,\height);
  \draw[step=1cm, line width=0.2mm, black] (0,0) grid (\width,\height);
  \draw[step=5cm, line width=0.35mm, black] (0,0) grid (\width,\height);
\end{tikzpicture}
\end{center}
\end{document}

The command \draw[step=2mm, line width=0.1mm, black!30!white] (0,0) grid (\width,\height) is used to draw a grid.
The step argument specifies the distance between the lines of the grid.
The line width argument specifies the thickness of the lines.
The black!30!white argument specifies the color of the lines as a blend of 30% black and 70% white.
The (0,0) argument specifies the starting point of the grid and (\width,\height) specifies the ending point, defined as (16,25).