Are you actually get .dwg files sent to you or simply PDF's of the drawings?
http://www.autodesk.com/products/dwg/viewers
http://www.autodesk.com/viewers/all-viewers
My company uses the BlueBeam Products. Have had nothing but nice things to say about my time with it so far.
I believe .shx files are fonts. The core file will be a .dwg file, the shx files were sent along because that font was used in the drawing. Autodesk has a free file viewer on their website, http://www.autodesk.com/products/dwg/viewers You want the DWG Trueview and will be able to print PDF from there.
I can't remember how or if batch plotting is possible from 2000 but you should be able to do it with Autodesk DWG Trueview. Are you trying to plt multiple files or layouts? Either way you can do it using Trueview.
There are several, but I can't recommend any of them here. Using third-parties opens a can of worms... sometimes literally. You can Google several, but there is always a risk of malware for free stuff. The Facebook idiom "If you aren't paying for a product you use, then you're the product being sold." comes into play there.
My recommendation is to use the 30-day full version trial of AutoCad, the .dwg viewer from Autodesk (you can view but not edit), or AutoCAD360 app for Android or Apple where you can manipulate files on your mobile device. I find the mobile product difficult to use without the precision and control of a mouse or wacom pad... but it's great for display and rudimentary editing.
DWG Trueview is a free autodesk product that will view and convert any version of dwg. I can't speak to the compatibility of all objects in 2013-14, but this could be a useful utility for you.
I see, so it's looking more like a software limitation to you then? Edge does have that feel on the i5 too which makes it a much more pleasing experience to navigate.
If you got time to take a look at something like these sample CAD drawings that would be great too: http://www.cadcamr2v.com/pages/sample_cad_drawings AEC drawing on the top, surprised this one will pan smoother than the panel dwgs for work I have open (guessing it's got to do w/ # of layers but I could be wrong), but nevertheless I get a bit of control lag when I zoom in to a medium zoom and start panning around. You can view this w/ Trueview from here: http://www.autodesk.com/products/dwg/viewers
Download TrueView from Autodesk to open and print your dwg & dxf files. As long as you can find the drivers for your particular plotter that are compatible with the version of Windows you are using, you can print from any program you want.
EDIT: This is not a CAD problem as much as a Windows driver problem. Your biggest challenge is going to be to find the correct drivers for that plotter. It is so old that it has probably not had a set of specific drivers written for it since probably XP, so you have your work cut out for you.
There are several ways to view, edit, and share .dwg files, the native file format for AutoCAD data files, without using AutoCAD software. One of them is DWG TrueView. This desktop software enables you to view .dwg files and includes DWG TrueConvert software, which lets you convert newer .dwg files to work with older versions of AutoCAD.
You're probably thinking of DWG Viewer? Either way, that page has both. I know, it's difficult to keep track of which is which when Autodesk wants to push everyone to using 360 instead.