Here's my personal review of the omake and grammar fixes that need to be made. I'll pick it piece by piece and point the mistakes out:
A black haired girl is currently sitting in a meditative position, willing her mana to move fluently in her body, gathering her mana in her hand, manipulating it to form a bright ball of Light, manipulating it to her will, she shapes it unto a spear-like form and then willing the energy-
*knock* *knock*
- The word "currently" is redundant and unrequired. The fact you are writing in the present tense is enough to inform the reader that this is happening as he reads the information.
- The sentence "sitting in a meditative position" can be shortened to "meditating," or "meditating on the ground."
- "willing her mana to move fluently in her body, gathering her mana in her hand," the second use of the words 'her mana' is redundant and repetitive. Simply use "it."
- "bright ball of
light." Not sure why you'd write it with a capital later.
- After the part above, it'd be better to start a new sentence that sounds more like this: "She manipulates her to her will, shaping it into a spear-like form and then willing the energy to move into other shapes, until she is interrupted."
*knock* *knock*
Bright blue eyes opened and fixed themselves at the sole door in the room.
"Elder Sister? Can I enter your room?"
"You may." replied the black-haired irritatingly.
"Um- uh..." The younger shift nervously under the glare of her Older Sister, no one interrupts her during her sessions after all unless it was their Father or an important matter.
Fortunately for the younger girl, it is the latter-
"*sigh* Speak, What is the matter?"
- *knock* is an onomatopoeia. A more professional way of showing onomatopoeias is to use caps-lock and/or use italics for the text. It should be:
KNOCK! KNOCK!
- No need to use capital letters in "elder sister," also, the term "elder sister," sounds weird.
- In "you may," the dot after "may" should be replaced with a comma (,) because the next letter continues the sentence.
- No need to capitalize father.
- The sigh shouldn't be an onomatopoeia, but a described action. As such: 'The girl sighs, "Speak, what is the matter?"'
"Ah! Yes ! Uh... Father said to prepare yourself for a visit to the Baragar Household!" replied the Younger Sister.
The black haired girl merely raise an eyebrow
"What caused Father to declare that suddenly?" replied the Elder Sister now a little bit more interested, The Baragar Family is quite a famous name in these lands after all and Father himself wished many times to get acquainted with them but did not find any opportunities. To say the Elder Sister was curious would be an understatement but as a proper lady from a famous mage house, she needs to keep her composure.
"Well, the Eldest Child of the Baragar Family just killed a Greater Dragon alone and Father want to use that as a way to get acquainted with them and possibly for you to-"
"To what?! I already told Father, I will choose the man of my life, it doesn't matter if he killed a Greater Dragon or not" scoffed the Elder Sister already forgetting her lady manners and start losing herself to her anger.
"*cough* She is actually a girl and the same age as you Elder Sister, he wished for you to become friend with her... He says that it will help him create a permanent relationship between our families" replied timidly the Younger black haired Sister.
"Oh... I'm sorry for my outburst... When are we leaving ?" The Eldest trying to blatantly change the topic not that her naive Little Sister noticed.
"Oh uh- As soon as possible! Father said that we are not the only one trying to get on the good side of the Baragar Family" replied the still nervous Sister.
"Good, come with me, I will choose for you a proper dress for our visit to the Baragar Household, it will be a taint to our name if we shamed ourselves in front of one of the most influential families of this land" replied elegantly the Elder Sister, quickly dragging her Sister by her arm.
"Eh ?! Wh- Wha- Sister !" replied the flustered girl, not having any chance from the start to escape from her fate as a dress doll for the next few hours.
- "Younger Sister," once again, shouldn't be capitalized. The proper grammar would be, simply: "younger sister."
- The black haired girl
rose an eyebrow, not "raise."
- Several more mistakes, but I'm too tired to point them out.
I can't fix any of them, because I can't edit other people's posts.