Going back to the first example, if you want to use an operator as a regular variable, use parentheses to disambiguate:
julia> 5 + 5
10
julia> · = 5
5
julia> ·
5
julia> (·) + (·)
10
If you need to check if something is a valid identifier, you can use Base.isidentifier.
If you need to check if something is an operator, you can use Base.isoperator, Base.isbinaryoperator and Base.isunaryoperator:
julia> Base.isidentifier("·")
false
julia> Base.isoperator("·")
true
julia> Base.isbinaryoperator(:·)
true