Your first question can be answered by a number of posts on this site, e.g., number format in pgfplots axis. The simple solution is to add code for number formatting to your axis labels:
/pgf/number format/1000 sep={}
Your second question can be resolved by setting ymin=0 (or really, any ymin value, 0 happens to be a good choice IMHO).
I would note that the \pgfplotsset line was giving errors for me, but I have no experience with context so I can't be sure what was causing the error.
The error on that line was due to using square braces instead of curly braces around the options. If I correct the error, the default ticks are overlapping, so in the code below is a specification of a reasonable number of ticks. You should change this as you see fit.
Finally, I prefer to end each line of the options (even the last one) with a comma. This makes adding new lines to the options easier - I don't have to remember to add a comma, and my version control only tells me that one line has changed, instead of two. So you'll see that here, but its purely personal preference :-)
\usemodule[tikz]
\usemodule[pgfplots]
\usepgfplotslibrary[statistics]
\pgfplotsset{width=12cm, compat=1.11}
\starttext
\starttikzpicture
\startaxis[y=1.5cm,
axis y line=none,
axis x line=bottom,
enlarge x limits,
thick,
x tick label style={
/pgf/number format/1000 sep={}
},
xtick={800,1200,...,3200},
ymin=0,
]
\addplot+[
green,line width=0.5mm,
boxplot prepared={
median=1500,
upper quartile=2500,
lower quartile=1200,
upper whisker=3000,
lower whisker=1000,
},
] coordinates {};
\stopaxis
\stoptikzpicture
\stoptext
