Hi@12Solutions,
Let's solve the problems one by one.
Q1: Based on the issue that you mentioned, do you want to make the SharePointIntegration display as a normal form or display a certain item?
A1:The form in PowerApps has its Edit mode by default, so if you do not have any records within your SP list, once you view the form in preview mode, it will show the "No item to display" message.
I assume that you want to create a new record, so you could add a "+" icon and set the OnSelect property as below:
NewForm(SharePointForm1)
Note: Please tab the "+" icon when you preview the form if you want to create a new record.
Q2: Do you want the "applied date" fields to appear when you select "applied for Drap" from a Lookup column?
A2: I found that the DataCardValue2 is a TextInput control which could not have a dropdown function, could you please check if you use another data card value to select the "applied for Drap"?
In my scenario, I have a Lookup column named "TestLookup" which is from a Text column in another SP list.
I have tested it in my scenario and I have the following formula that works great.
If(DataCardValue3.Selected.Value ="Card 1",true,false)
The Items property of my DataCardValue3 is set as below:
Choices([@TestBlank].TestLookup)

Regards,
Qi