Hello,

I believe 1/1/0001 could be returned when a DataMode.Date is used but the date is actually null instead of a particular one. 

There are several options to tie the igDatePicker with some data. For rendering, Let’s assume you are using a IgniteUI Razor template and have the following auto–generated code. I am adding the Birthdate prop, and extending the Customers list with the additional property details.

Models:
    public class Customer
    {
        public int ID { get; set; }
        public string Name { get; set; }
        public bool IsActive { get; set; }
        public DateTime Birthdate { get; set; }
    }
    public class CustomersViewModel
    {
        public IEnumerable<Customer> Customers { get; set; }
        public IEnumerable<CustomerCountSummary> CustomerCountSummaries { get; set; }
    } 
View:
@using Infragistics.Web.Mvc
@model InfragisticsMvcApp1.Models.CustomersViewModel 

    <h3> DatePickerFor Editor</h3>
        @(Html.Infragistics().DatePickerFor(m => m.Customers.FirstOrDefault().Birthdate)
         .DataMode(DateTimeEditorDataMode.Date)
         .ID("datePicker3")
         .Render()
        )

Controller:
        public ActionResult Index()
        {
            var viewModel = new CustomersViewModel
            {
                //IEnumerable of Customer Objects
                Customers = GetCustomers(),
            };
            return View(viewModel);

        }

        private IEnumerable<Customer> GetCustomers()
        {
            return new List<Customer>
            {
                new Customer { ID=1, Name="John Smith", IsActive=true, Birthdate=new System.DateTime(2020,12,05) },
                new Customer { ID=2, Name="Bob Richards", IsActive=false, Birthdate=new System.DateTime(2020,12,06) },
                new Customer { ID=3, Name="Marge Wright", IsActive=false,Birthdate=new System.DateTime(2020,12,07) },
                new Customer { ID=4, Name="Dwight Long", IsActive=true, Birthdate=new System.DateTime(2020,12,08) },
                new Customer { ID=5, Name="Amy Grant", IsActive=true, Birthdate=new System.DateTime(2020,12,09) },
            };
        }

Here datePicker3 will be tied to the first Customer object and have 2020,12,05 date rendered.

Another approach could be to use a single data object/Customer and bind to
Controller:
Customer someCustomer = new Customer { ID = 1, Name = "John Smith", IsActive = true, Birthdate = new System.DateTime(2020, 12, 05) };
return View(someCustomer);

View:
@model InfragisticsMvcApp1.Models.Customer
    @(Html.Infragistics().DatePickerFor(m=>m.Birthdate)
         .DataMode(DateTimeEditorDataMode.Date)
         .ID("datePicker2")
         .Render()
    )
 

What is more, Updating the Model will be depending on your implementation and as it is more like a general MVC question, you could refer to MVC update model resources on the net. A random one for example:
http://www.joe-stevens.com/2010/02/17/asp-net-mvc-using-controller-updatemodel-when-using-a-viewmodel/