The first part of the translation looks pretty good. So let me give a try to the final part. 

I corrected characters and spellings. Also the last comma, which was missing, is important to the meaning. It would be better if ´sadece´ was placed after ´ömürboyu´ in the original text.

Hatıra could mean ´reminder´ but I assumed that two people haven´t seen each other in real life. So I took the literal meaning of ´memories´.  Although I´m not sure if this assumtion was correct.  

"İçimde sadece ömürboyu mukemmel aşkım olarak kalacaksın. Senden hiçbir beklentim yok.  Sadece seni tanımak istemiştim ve bende hiçbir hatıran olmadığı için bir de fotoğrafını,  ilerde bakabilmek için... "

You will remain lifelong inside me only as my perfect love. I don´t have any expectations from you. I only wanted to know you better. Also I wanted a picture of you so I could look at it in the future, because I don´t have any memories with you.

I didn´t write to you because I´m in love with you or because I want you back.

If that was the case I wouldn´t have left you.

I just missed an old friend, that´s all. It´s good to hear that you are happy.

Doudi, there is an example. If you check the example again you should be able to figure out how to complete that section for next week.

Have a look here:

http://www.turkishclass.com/tl_homework_assignment.php?homework_id=21

This is a different noun state. It´s called accusative case.

-e dative

-de locative

-den ablative

-i accusative

Also, there is a mistake in tjis sentence: 

Sen Ankara´yı seviyor musun?

Merhaba Christine,

It is called accusative case. It is part of beginner 1 lessons.

http://www.turkishclass.com/tl_homework_assignment.php?homework_id=21 

Here is the correct link:

http://ipb.nu/winmekmak/

Here is an online conjugation tool (although I suggest winmekmak):

http://www.verbix.com/languages/turkish.shtml

"Over all, i understand it,something like day come, i will make you a favor´"

It is very good that you understand the meaning of sentences. Don´t worry about the details that you don´t understand. Just continue reading and read more and more. We are talking here of more than 1000 pages. This could take 6 months.

Also extensive dictionary work is needed. You might need to check the dictionary twenty times in one page. With time as your vocabulary improves the number of unknown words per page will drop.

Possibly you should read stories that you like and would remember. If you can find something in a dictionary that´s fine. If you can´t find it, underline it or take notes and continue reading but don´t interrupt reading. More flexibility is needed.

A foreign language can be very different than yours. Many things might not make sense. Things could be in a completely different nature. If you simply accept that and move on, then it will be better. If you stop and fight with it until makes more sense in your language, then it will not be so good.   

It is a very good idea to read the same text again but only after a while. I would say second readings should be done at least after two months. 

In those sentences the only thing that you need to know is that anlamak takes -i case.

-i anlamak, bir şeyi anlamak : to undertstand something.

Instead "nihayet" I would suggest "son olarak" ( lastly ). For "evvela" you could use "önce" or "ilk önce" or "ilk olarak" ( firstly ). Bye.

Gezbelle, if we would help you, wouldn´t this be cheating? In general you did well. There are a couple of mistakes here and there but it is better to leave them so your teacher can see them and focus on these areas.

By the way, "evvela" and "nihayet" are a bit old fashioned. Did you pick these words?

Londra´u has two vowels but two vowels don´t come next to each other. Besides it doesn´t have the correct vowel according vowel harmony. İstanbul´u is correct.

Canlı, verbs take different case suffixes to their objects. These are pre defined. They don´t change.  

For instance sevmek always takes -i case.

Ali okulu seviyor.

Ayşe tenis oynamayı seviyor.

Başlamak (to start something) always takes -e case.

Ben okula başladım.

Ben tenis oynamaya başladım.

"Hoşlanmak" (to like) always takes the -den case.

Ben okuldan hiç hoşlanmıyorum.

Ben tenis oynamaktan hiç hoşlanmıyorum.

In these three sentence "tenis oynamak" is the object. It is not different than any other object. You might be confused to see that "oynamak" takes all case suffixes just like an ordinary noun. Is "oynamak" a noun? The answer is yes. Infinitives are the names of verbs. Because they are names they are nouns. They become verbs when they are conjugated.

The infinitive is the noun form of a verb. The short infinitive (-me, ma) isn´t any different than the long infinitive (mek, mak) except that with most noun cases (dative , accusative) we use the short infinitive. Also the short infinitive can create permanent nouns that are used in compound nouns.

Here are some more examples with the short and long infinitives that take case suffixes :

Ben okumayı seviyorum.

Ben okumaya başladım.

Ben kitap okumaktan hoşlanıyorum.

Reading is a good idea. I wouldn´t worry about grammar as long as you understood half of what you are reading. It is more important to continue reading and to read lots more than studying grammar. You will learn many grammar points intuitionally with time. Plus you will learn lots of vocabulary and you will get used to sentence structures. The only thing I would worry would be to find something to read that I would like reading.