First off, get the laptop with the new windows 10 up and running, so many websites including banking, youtube and many image websites only work with win 10. You may want to use the laptop for your facebook and to view images.
Nothing wrong with the old dell PCs, if you keep them clean they could last forever
What windows version does your PC dell use? if it's windows 8 or 8.1, that is why the images on facebook are blank. You just spent money on the fix, can you call the person back and tell him to fix the image issue?
This PC I use now has windows 8.1, it's an excellent gaming computer. 8.1 will not show images from some image websites and some websites like my bank won't work with windows 8.1.
On the Microsoft website they have an upgrade for windows 8.1 called "Microsoft Edge". I have Microsoft edge installed on this computer and use the ms edge browser for any websites that don't work with plain fast windows 8.1. yes you can use both versions separately on one computer.
1) did the repair person upgrade your PC windows to 8.1? if so install "Microsoft edge for windows 8.1"
2) open that laptop and try to learn to use the windows 10, use 2 computers at the same time. One can play music or movies while you play on the other
3) that modem is old but if it works for you no need to change. usually your isp charges a fee per month to use their modem. If they do charge a fee they should provide you with a free upgraded modem if you ever need one.
4) 400$ isn't to bad to have someone come to your house and work on 2? computers. But the work should cover adjusting both computers so they work the way your need them to- like viewing pictures on facebook.
Good luck!