Mon premier journal/ma première entrée de journal

Technically what you've written is "une entrée de journal" (a journal entry). Both words are accepted in the LC context, but it's better for you to know the accurate terms

C'est monla premièrer fois ecrire danque j'écris une journal sur ce site.

The structure in French is literally: "it's the first time that I do something"
You wrote a journal on this website = j'écris un journal sur ce site

J'espeère ilque ça améliorerai mon français .

Whole verbal groups, like "écrire" un journal, can only be repeated using "ça" (in some very rare cases, "il", but these are exceptions)
ça => améliorera
Subordinating conjunctions are compulsory in French => j'espère QUE...

Je viens de 'Irlande et j'ai eétudié le français pour(pendant) cinq ans quand j'ai été dansétais à l'eécole.

de+vowel => d'
Duration is almost never expressed using "for". "Pendant/durant" (or nothing at all, in most cases) are used instead.
"à/dans l'école" is the same difference as "at vs in (the) school"

MaintenantDepuis, j'ai oublieé plus de français que je mene m'en souviens.

If you want to refer to a "forgetting" action that has started in the past and has been going on until today, you can use this structure
depuis = since (that time)
en = du français (se souvenir DE quelque chose)