Ich lud eine Freundin von mir als einer Veganerin ein. Ich bereite jetzt die Speisen vor. Aber ich bin nicht sicher, ob ich gute Speisen kochen kann, weil ich die Fleischspeisen liebe. 

You did a great job☆ There are nearly no grammatical failures. Keep going☆
I know what you want to say but the expression is a little bit confusing. 
In the first sentence it sounds like you are a vegan or you want your friend to be a vegan. I would suggest to say:
Ich lud eine vegane Freundin von mir ein. 
Or
Ich lud eine Freundin von mir ein, die eine Vegetarerin ist.  (By the way it is really cool you use the past from " einladen"= "lud...ein" but If you want you can also use the perfect like the most German to tell something you did. Then it would be: Ich habe eine vegane Freundin von mir eingeladen.)
 For the other sentences you can use the word "Speisen" everbody will understand you but you will sound a little bit like a servant in a noble house hundreds of years ago, so the word is a little bit old. I would suggest to use the word "Gericht"(=meal) instead.
You can ask me if you still have some questions. I will answer them with pleasure.
I hope everthing will be fine with the invetation of your vegan friend^^