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Well, actually I didn't use `SqlAdapter` to work with DB since I prefer using ORM or write everything by myself (without `DataSet`, `DataTable`, `SqlAdapter`, etc) but I still can give some advices.

Here, you have mixed 2 separate questions:

* How to update data in a db from C#
* How to update UI with respect to changes in a db

When you split your "big" task apart it gets easier to find an answer separately.

Comments regarding the first "part":

1. You have to open connection:

```cs
con.Open();
```

2. To apply `Update` command you can use [`ExecuteNonQuery`](https://docs.microsoft.com/en-us/dotnet/api/system.data.sqlclient.sqlcommand.executenonquery?view=dotnet-plat-ext-5.0) method:

```cs
cmd.ExecuteNonQuery(); // ignore the result for now
```

That's it!


And now we can move further to populating `GridView`. Check docs to read how to do it via [SqlDataAdapter](https://docs.microsoft.com/en-us/dotnet/api/system.data.sqlclient.sqldataadapter?view=dotnet-plat-ext-5.0) class.

```cs
// update db
var connectionString = Properties.Settings.Default.dbConnectionString;
using (var con = new SqlConnection(connectionString))
{
    con.Open();
    using (var cmd = con.CreateCommand())
    {
        cmd.CommandText = @"UPDATE CUSTOMERS SET " +
                    "CustomerId = @CustomerId, " +
                    "FirstName = @FirstName, " +
                    "LastName = @LastName, " +
                    "Email = @Email, " +
                    "Height = @Height, " +
                    "DateOfBirth = @DateOfBirth ";
        cmd.Parameters.Add("@CustomerId", SqlDbType.Int, 5, "StudentID");
        cmd.Parameters.Add("@FirstName", SqlDbType.VarChar, 50, "FirstName");
        cmd.Parameters.Add("@LastName", SqlDbType.VarChar, 50, "LastName");
        cmd.Parameters.Add("@Email", SqlDbType.VarChar, 1, "Email");
        cmd.Parameters.Add("@Height", SqlDbType.Int, 50, "Height");
        cmd.Parameters.Add("@DateOfBirth", SqlDbType.Date, 10, "DateOfBith");

        cmd.ExecuteNonQuery();
    }
}

// update ui
var sql = "SELECT * FROM CUSTOMERS";
using (var con = new SqlConnection(connectionString))
{
    con.Open();
                
    var adapter = new SqlDataAdapter(sql, con);
    var ds = new DataSet();
    adapter.Fill(ds);

    gridView1.DataSource = ds.Tables[0];
}
```

Side note: I've suggest you moving db related code into a separate project and call methods from there. With current approach when everything in UI-layer your code become messy very quickly.