No. The wish always concerns 3rd person sg (gün).

So literally the phrase is

                        May (your, his) birthday be happy.

My Try:

Is This a Zoo, Am I a Monkey Or What?

Şahin Irmak got mad when he was fotographed while sitting in a Nişantası cafe with his girlfriend on the previous day.

Şahin Irmak was in a place called Hardal in Nişantaşı on the previous day. The famous actor who was deep in a conversation with his girlfriend was tensed when he noticed some reporters. Irmak shouted: "Why are you taking pictures of me? Is this a zoo, am I a monkey?" Later he took his girlfriend who tried to hide his face behind her hair and left.

You also call them eggs? So do we. =)

Evet HaNNo.

(Just remember making deverbal nouns doesn´t work with every verb this way. The use of derivational suffixes is limited and unpredictable.)

doğum is like bilim or ölüm, it is a noun made of a verb root.

                öl|mek ´to die´ > öl|üm ´death´

                bil|mek ´to know´ > bil|im ´knowledge´

                doğ|mak ´to be born´ > doğ|um ´birth´

-Im is not a 1st person possessive suffix in doğum but a derivational suffix. So it doesn´t chance.

2nd person sg shows in gün|ün ´your day´.

The predicate takes the past tense marking. Here the adjective/adverbial is the predicate (i.e. is saying something about the subject).

What a relief. Does someone still want to claim Muslims are backward people?

MyTry:

Which animal were you while saying I´ll spend a lifetime with you? A butterfly?

Which aminal were you while saying I will love you till I die? A butterfly?

(Referring to the short life of a butterfly. The context is smart aleck.)

You have a funny strategy of introducing a package of suffixes without explaining what suffixes they are like

                  Verb + seydi/saydı , verb + erdi / ardı / irdi / ırdı / urdu / ürdü

It might work. Especially with learners who have the chance to use Turkish a lot. Instead of detailed grammatical analyses they just gather these packages to their mind.

But when are your students going to learn vowel harmony? Are you going to explain it over and over until doomsday?

My Try:

I love crash of thunder. Maybe it´s because it roars on my behalf also.