Dear chiquita79,
´First � is an Ordinal Number - ´first �, ´second �, ´third �, etc.
´At first � = ´At the beginning �; ´In the initial stage, or in the initial stages �.
"At first, Nikki tried to be patient, but later ... ... "
´Firstly � is an Adverb.
´Firstly � = to give the first reason; the introductory point; the first point in an argument.
"Firstly, I did not take your ham sandwich; secondly, I don ´t like ham; thirdly, your sandwiches are disgusting; ... ..."
´In the end � = ´eventually; or ´on reflection �; or ´after thinking about it �.
"I had a big argument with Petra but, in the end, I realised that she was right, so I apologised to her!"
1) ´Finally � is at the opposite end to ´Firstly � in an argument.
"Firstly, I did not take your ham sandwich; secondly, I don ´t like ham; thirdly, your sandwiches are disgusting; finally, I saw Chiquita eating your sandwich!"
2) ´Finally � is used at the end of a long argument to make a final point, or at the end of a speech.
"Finally, thank you for inviting me here this evening. Goodnight!"
3) ´Finally � is used to end doubt or argument.
"I wish to state finally, that my Client is innocent of this crime".
4) ´Finally � is used to mean ´After a long time �, (especially when there have been problems or difficulties).
"Finally, we have paid all of our debts, and now our firm is in Credit again!"
I hope that this helps you.
Les