The previous FoxyProxy, which you've been using for 5 years, had those permissions and even more: in fact, it had unfettered access to your entire computer (just like every other legacy Firefox addon). It had the ability format your hard drive or steal your passwords. That's because Firefox 56 and earlier didn't have restrictions for addons... at all. The new version of FoxyProxy is much more restricted because of this permissions system.
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Permission to "download files" is required for exporting your settings to a file (which you can then share to other devices for importing). That is how Firefox chose to allow add-ons to write to the local filesytem: you have to trick Firefox into thinking that writing a file (your exported settings) is really a download. The "download history" permission is required simply because Firefox does not allow add-ons to specify just "download files" without "download history". Internally, nothing is done with download history. This is open source software and you can view the code yourself at https://code.getfoxyproxy.org