This is an old question, but answering for gathering knowledge.
We have an original form with a button to show the new form.

The code for the button click is below
private void button1_Click(object sender, EventArgs e)
{
New_Form new_Form = new New_Form();
new_Form.Show();
}
Now when click is made, New Form is shown. Since, you want to hide after 2 seconds we are adding a onload event to the new form designer
this.Load += new System.EventHandler(this.OnPageLoad);
This OnPageLoad function runs when that form is loaded
In NewForm.cs ,
public partial class New_Form : Form
{
private Timer formClosingTimer;
private void OnPageLoad(object sender, EventArgs e)
{
formClosingTimer = new Timer(); // Creating a new timer
formClosingTimer.Tick += new EventHandler(CloseForm); // Defining tick event to invoke after a time period
formClosingTimer.Interval = 2000; // Time Interval in miliseconds
formClosingTimer.Start(); // Starting a timer
}
private void CloseForm(object sender, EventArgs e)
{
formClosingTimer.Stop(); // Stoping timer. If we dont stop, function will be triggered in regular intervals
this.Close(); // Closing the current form
}
}
In this new form , a timer is used to invoke a method which closes that form.
Here is the new form which automatically closes after 2 seconds, we will be able operate on both the forms where no interference between those two forms.

For your knowledge,
form.close()
will free the memory and we can never interact with that form again
form.hide()
will just hide the form, where the code part can still run
For more details about timer refer this link, https://learn.microsoft.com/en-us/dotnet/api/system.timers.timer?view=netframework-4.7.2