CheckFormMode.cs

//check if page is in edit mode through page form mode
if (Microsoft.SharePoint.SPContext.Current.FormContext.FormMode == SPControlMode.Display)
{
  // your code to support display mode
}
else if(Microsoft.SharePoint.SPContext.Current.FormContext.FormMode = SPControlMode.Edit)
{
  // your code to support edit mode
}

CheckPageMode.js

function checkIfEditMode()
{
    //check if page is in edit mode through javascript
    //must support SP2010, SP2013, publishing pages and wiki pages

    //publishing page
    if (document.forms[MSOWebPartPageFormName].MSOLayout_InDesignMode !== undefined)
    {
        //console.log("publishing page found!");
        var inDesignMode = document.forms[MSOWebPartPageFormName].MSOLayout_InDesignMode.value;
        if(inDesignMode === "1")
        {
            console.log("publishing edit mode active");
        }
    }
    else
    {
        //wiki page
        if (document.forms[MSOWebPartPageFormName]._wikiPageMode !== undefined) {
            //console.log("wikiw page found!");
            var wikiInEditMode = document.forms[MSOWebPartPageFormName].MSOLayout_InDesignMode.value;
            if (wikiInEditMode === "Edit") {
                console.log("wiki edit mode active");
            }
        }
    }
    
}

CheckWebPartMode.cs

//check if page is in edit mode through webpart settings
WebPartManager wp = WebPartManager.GetCurrentWebPartManager(Page);

if (wp.DisplayMode == WebPartManager.BrowseDisplayMode)
btnLink.InnerText = "Edit Page";
else if (wp.DisplayMode == WebPartManager.DesignDisplayMode)
btnLink.InnerText = "Exit Edit Mode";
else
btnLink.Visible = false;