Being a mac user and sometimes linux user (never Windows), I miss Visio since that's how I created my diagrams.  I tried many different software replacements to just be let down.  I stumbled on lucid.app which my initial reaction was, no way a web based anything could come close to Visio but man was I wrong.

Yes you can import stencils

Yes you can import Visio diagrams, OmniGraffle, Gliffy, Draw.io

Yes you can export Visio

Is it free?  No but its very affordable or I wouldn't be using it.  I haven't done the compare in cost but I'm fairly confident it's less expensive than the subscription to Visio and no obligation.  As you can see I use the Individual plan which runs $95/year but includes more than enough to be a competitor with Visio and other similar tools.