I'd say to really figure this one, I would run wireshark on two of the machines that can't talk to each other and capture on both and look at the captures to determine what is causing the issue. If you can get the capture files, you can PM them to me and I can look if you don't want them available publicly.
>>>Well, yes, that's a normal Microsoft design function; they only want you to use their OS for free networking. However, there's usually a way to do a workaround, though that usually involves building a Microsoft server such as 2008 Server RT or newer. Multi-protocol environments are then allowed to be added onto the NT kernel going all the way back to NT v3.51 as additional purchased services (more money for MS). Normal home users do not use Linux, just like they don't use VMS or Solaris. In fact Home Networking doesn't play nice with Mac iOS either, as you said they aren't designed to work together in a peer-to-peer LAN environment; they never were.Yes, the default "upgrade" pushed out to XP users is Windows 10 Home. W10 Homegroup isn't usable as it is designed to block the other OSes I use. Shares don't work properly on a mixed network if Windows is allowed to use Homegroup, but fortunately even W10 can use normal shares.
This sounds like a "Microsoft" solution - re-install all the operating systems!
Microsoft would say that you are attempting to apply a business level solution to a consumer-use product which they never intended, especially without getting paid for that capability in your OS.
And since you're using Linux and Windows in a multi-OS network, I don't suspect putting in a server in your home environment is anywhere on your visualized horizon.<<<
You might still try to use a different version of Linux such as Ubuntu or Puppy-Linux on your machine running the Mint; if you have a spare hard drive you could remove the drive with Mint, stick it in a drawer temporarily and put in the spare drive and install Ubuntu or one of the other many Linux versions as I refer to in my Post #14 and see if those Linux versions can use shares on the W10 systems you have over the network. We still haven't heard from any of our Linux gurus on this topic or perhaps they haven't tried Mint with W10 over the network; but if you decide to try it and it works with Ubuntu or one of the other Linux versions, please post back and let us know so we can share that with other forum users.