When it comes to the Roku, you may need to turn off, or at least pause, the Video Data Saver. Either this or turn the resolution down for your streaming, which I don't know if you can do with a Roku (I don't have one).
Something else that may help is power cycling your modem. To do so, unplug the modem at either the wall outlet or the power pack (DO NOT remove the plug at the back of the modem). After waiting at least a minute, plug the modem back in. Then, after waiting at least five minutes, which will give the modem time to fully boot and be ready, try your activity again. Again, this may or may not help, but it sometimes does, so it's worth a try.
When it comes to speed issues, even when it concerns only specific sites and such, the reps will normally need some speed test results, even if those results are showing that you're getting decent speed, as they can glean more from the results than just your overall speed. But, with you not having a LAN cable connectible computer to be able to run the speed tests, it would be best to wait until a rep replies to see whether they're needed, and if so, how they could be run.
The reps are on M-F from approximately 9AM to 5PM EST, so the earliest you'll hear from one is tomorrow.
I'm hoping that the reps reply today in order to figure out what may be going on. Though I don't know if this is the case, it could be a weak WiFi connection to your TV that's causing the discrepancy, but the reps should be able to see if this is the case if they run remote diagnostics on your HughesNet equipment, which they normally do in the course of troubleshooting. The problem with the websites might be related to whatever is causing the problem with the TV, but it's hard to know.
Though they'd normally see this thread in the course of checking for new topics, I'll tag a couple of reps, just in case. This way they will surely see it.
In the meantime, if you normally don't, it would be a good idea to leave your modem plugged in so that the reps can run the aforementioned remote diagnostics on your HughesNet equipment, if they deem it necessary.
Thank you for reaching out to us. I'm sorry to hear you are experiencing this. After running diagnostics on your equipment, It appears the equipment is fully operational and your modem is reporting speeds similar to what you stated you were getting. I do see that there is an unknown device connected to the network with a poor signal. The mac address begins with this 00:3d:e8. I believe this may be an LG smartphone. You can improve the singal quality by moving the device closer to the modem.
In regards to Prime Video not working, I recommend taking a look at the methods listed on this website. Not all will be applicable as you have already done some of these https://streamdiag.com/amazon-error-insufficient-bandwidth-fix/.
When I open the Prime Video app on the TV, I get a message that my internet connection is not available. However, I noticed one day that if I left it there for a few minutes it came on. I've only seen this once and haven't had a chance to try it more. Would this possibly be due to the higher latency?
It's possible that the latency could be causing an issue, though if it's not higher than normal that shouldn't be the case. Though I hadn't yet tried it on my own TV, I just did so and it worked without issue, though this was only my own test and your network could be having issues that mine is not.
Do you have any other apps on your TV that you can try to see if the problem might be with Amazon Prime Video itself? If not, or you do, but they don't work either, do you have a different LAN cable that you might be able to try, at least just on a temporary basis to see if that could be the problem?
It's also possible that there is an issue somewhere down the line in the connection to Amazon. If you know how to run a traceroute, it wouldn't hurt to do so to amazon.com. If you don't know how to do so, see the following...
If you run Windows, run a command window from Windows System > Command Prompt in the Windows menu and type:
If you run Mac or Linux, bring up a terminal window (terminal.app) and type:
Then copy/paste the results here.
The results should show if there is some sort of issue that's causing high latency or some other issue along the path. Granted, I'm not very versed in reading the results of traceroutes, other than seeing high latency, but others are, like @MarkJFine. If there is some sort of issue, he may be able to tell you what it is, or where it is, by looking at the results of the traceroute.