Hi there. Comparing with a typical Romance language (your native language), German has a very strict rule regarding the position of verbs. Typically, except for imperatives and interrogations, the main conjugated verb (or auxiliary verb) has to be placed at the SECOND position inside a main clause(sentence), while it has to be placed at the LAST position in a sub-ordinate clause. On the other hand, any infinitive or past particle has to be placed at the LAST position in a main clause, and at the SECOND LAST position in a sub-ordinate clause. To this extent, you can see that the infinitives "mitkommen", "treffen" and "essen" did not follow the above rules. This means that you need to pay more attention in the aspect before your upcoming language test in German.
For the conjunction such as "und", "oder", "aber" and "sondern", etc., it is generally preceded by a comma, in order to separate between the two main clauses. Thus, "In meine Firma gibt es ein Problem, und ich muss am Samstag ..."
Although the first respondent has provided the corrections in very good details, he has probably missed the points regarding the letter writing in German (based on my limited knowledge in this language) that,
1) One must start with a word in non-capital letter, because it follows the comma after you have addressed your addressee. Therefore, it is correct to write "Lieber Christian, entschuldigung, aber ..." (unless there were recent rule changes in German, of which I am not aware).
2) One usually uses the capitalized letter for the 2nd personal pronouns (in singular "du" or plural "ihr" form) in order to show respect to your addressee. Thus, you should write "Du", "Dich", "Dir", and "Dein/Dein/Deine..., etc." (for possessive in nominative), and "Ihr", "Euch", "Euch", and "Euer/Euer/Eure..., etc.", regardless the position of such pronouns. (Ich warte auf Deine Antwort) [It is however not a strict rule, just in general.]
Good luck / Viel Gruß / Buena suerte.