I have a need and the resources to host websites for development/testing. Can my users access these ssites via internet-over-satellite using this business service ?
The acceptable use policy can be found here: https://www.exede.com/documents/master/acceptable-use-policy.pdf Having your own site is not a violation but, other things that might be done on that site could be. Read the policy, be sure you don't need an Enterprise or, Business account before you proceed. If you have further questions, please email them to firstname.lastname@example.org, someone in corporate will be able to answer your questions and, keep you form getting in trouble.
Not sure if viasat offers static ip's, you'll likely need that for your web host. Then configure your server with cloudflare (free) to get better delivery to your visitors. ( I recommend buying a hosting package, i use a2hosting and am very pleased with it. also smarterasp is a really good host too)
Almost all hosting sites (especially the cheap ones) will host database servers on different machines which really slows down performance. And while you may get a non-shared web server, you're not going to get a dedicated database server unless you pop for a dedicated server.