Those are basically the same meaning and even I don't differentiate those for a business email. But here are just my opinion about this.
1) 申請を確認していただき、ありがとうございます。
This sounds like you asked someone at first.
She/He has done it like you asked them.
And you appreciate it.
2) 申請を確認していただいて、ありがとうございます。
99.9% same meaning as the first one.
But this sounds 0.1% more casual.
3) 申請を確認して下さって、ありがとうございます。
This sounds like he/she did something for you even though you didn't ask anything to them in advance.
Like I told you, you don't have to think the difference among them.
All those are very polite and formal.
And I would say "申請状況を確認して下さり、ありがとうございました。"