Your case 1 "I have submitted" indicates that the act of submission occurred at some unspecified time in the past.
Case 2 "I submitted" indicates that the act of submitting the information is complete -- in this case, completed shortly before the person signs. I have not been able to think of a context in which the meanings of cases 1 and 2 would be meaningfully different, using this construction.
Case 3 "I am submitting" says that the submission is in the process of happening. In this case I would interpret it as saying that the act of signing the form is also that act of submitting the information, or perhaps the act of transmitting the signed form is the act of submitting the information. This is technically different, but the difference has no practical effect in this instance.
In general the past perfect deals with actions already completed, and normally with actions completed before some other past action. Here there is no other action to compare with. However (case 1) is actually the present perfect, which is used either for actions started in the past and continuing to the present, or for actions performed at an indefinite time in the past. Here the indefinite time would seem to be meant. The simple past (case 2) deals with action at some time in the past. It does not specify time relative to another action, but is normally used or completed actions. Most things expressed with the past perfect can also be expressed with the simple past, perhaps losing some nuance and any indication of relative timing of events. The present continuous tense (case 3) deals with actions in progress.
by the way "will constitute in having my application rejected" is ungrammatical. I suspect that "will result in" is intended.