1) I think "click on" is a little more formal than just "click", but either is correct.
2) Neither is great.
The first sentence is wrong, it should be "write back with", as in the second sentence, not just "write back".
However, the phrase "write back" tends to be more associated with physical letters than anything else. It's not incorrect, but a native speaker is far more likely to use the word "reply".
So, "In order to better assist you, please reply with the following information:"
"In order to better assist you, please provide the following information:" (as Bill suggested in his answer) is also a good way of wording it.
Asking them to "provide the" reads as a little more formal than "reply with the", but neither sentence is particularly informal.