If value is null put an empty string on razor template?

This is exactly what the NullDisplayText property on [DisplayFormat] attribute is for.

Add this directly on your model:

[DisplayFormat(NullDisplayText="", ApplyFormatInEditMode=true)]
public string EMail { get; set; }

To Check some property of a model in cshtml.

@if(!string.IsNullOrEmpty(Model.CUSTOM_PROPERTY))
{
    <p>@Model.CUSTOM_PROPERTY</p>
}
else
{
    <p> - </p>
}

so best way to do this:

@(Model.CUSTOM_PROPERTY ?? "-")

If sounds like you just want:

@(UIManager.Member == null ? "" : UIManager.Member.Email)

Note the locations of the brackets is critical; with razor, @(....) defines an explicit range to the code - hence anything outside the brackets is treated as markup (not code).