Question

My name is Katherine Mendoza, and I am a Master Student in Public Health Management at the Institute for Applied Sciences. I have been in contact with Dr. xxxx about *1 the possibility to do my internship at your institution, in topics related with the PHM *2 program.
When I was *3 reviewing the institute´s webpage, I noticed about the open position *4 for research assistant. I would like to apply to this position, but unfortunately I am unavailable until after first the week of July, when I expect to finish my theoretical studies.
I would like to know if it is possible to apply, considering my actual availability. Please, find my attached CV *5. If *6 you need further information, please do not hesitate to contact me.
I look forward to hearing from you. 

Kind regards

Very well written. The following are simply suggestions to enhance level of professionalism. Avoid abbreviations/ contractions.

*1 = "regarding" the possibility

*2 = spell out "Public Health Management" 

*3 = "Upon"

*4 = "vacancy"

*5 = " I have attached my cover letter"

*6 = "Should"

Question

My name is Katherine Mendoza, a Master's student in of Public Health Management in at the Institute for Applied Sciences., I have been in contact with Dr. xxxx about the possibility of doing to do my internship in at your institution, on topics related to with the PHM program.
When I was reviewing the Institute´s webpage, I noticed about the open position for a research assistant. I would like to apply for to this position, but unfortunately I will not can not be available after the first the week of July, I am date that is expected to finish my theoretical studies.
I would like to known if it´s possible to be considered for the position according to my  apply, considering my actual availability. Please, find attached my CV attached. If your need further information, don´t hesitate to contact me.
Looking forward to hearing from you. 

Kind regards,

Question

My name is Katherine Mendoza, a Master Student in Public Health Management in the Institute for Applied Sciences.  I have been in contact with dr. xxxx about the possibility of doing to do my internship in your institution, in topics related with to the PHM program.
When While I was reviewing the Institute´s webpage, I noticed about the open position for a Research Assistant. I would like to apply to for this position, but unfortunately I can will not be available after the first the week of July, the date when that is I expected to finish my theoretical studies.
I would like to known if it is possible to apply , considering my (actual) availability.

Please find attached my CV. If your need further information, please feel free [do not hesitate] to contact me.
I looking forward to hearing from you

Kind regards