Welcome to the forum!
It sounds like you are having 2 problems, right? If not, then I don't understand how the printing size is related to email.
I'm not familiar with "screen printer". Is it for screen printing, like putting designs on t-shirts? Or is it something similar to the Prt Scr key?
You can find your Inkscape version by Help menu > About Inkscape. The version might be especially important for your problem of printing at the correct size, because Inkscape has recently changed it's native DPI from 90 to 96. And there are some new settings to deal with for this too.
EPS (if I remember correctly) can containg both raster and vector contents. Before you send the EPS file, have you double-checked that the file you sent was all vector? I won't be able to help much for testing, because I'm not set up to open EPS files.
If they in fact were sent as vector images, I don't know how they could have been changed by emailing them. As far as I know, files are never opened during emailing. How could the content be changed without accessing it?