I have applied to a Phd position , where they require a certificate for my English skills. I did the TOEFL exam and just received my score. I downloaded the report as a PDF and was thinking whether it is permitted to send this PDF file directly to the University or is it just allowed to send it using TOEFL service (-> report will be sent via post to the university by TOEFL )

I don't think it would make much difference? They will either accept it or wait to receive it from TOEFL

Along with speaking fluently, you need to excel listening and writing exam as well when it comes to get good score at IELTS. I was not good at writing so I preferred getting the professional ielts coaching in panchkula. They not only help to me improve the writing skills but they provided me great tips for passing other parts as well. https://marveledu.com/