1. I request you to explain me what should be the role of this Special personality / Guru / Master mentioned by our Babuji, with respect to our Sadhana or in the methods of Meditation we do and what exactly is the "Connection" with him.
The connection with our beloved Master who is also the Special Personality is what is given at the time of introduction into our system of practice. He is our Guide/Guru/Master. The Special Personality has many other things to do than training us and that is the work He discharges to Nature as per the need and command from Nature.

2. It is appropriate to consider You / Trainer / Babuji (But physically only You are available to us) as my Master or Guru who will help for my Spiritual progress and also meaningful for some of the Methods we follow like receiving "Sacred current entering our hearts during the Cleaning process and Pranahuti during Satsanghs and Individual sittings".
It is the Master alone who helps the aspirant. The trainers according to the level of their approach assist the aspirant to move in the spiritual path. However the Pranahuti offered is always from the Source or Divine only. The following example however crude it might be will be useful to understand. The power from the hydel project is the same: yet it works in a bulb, fan or oven in different varieties. Similarly the power of Pranahuti is the same but the trainers modulate it according to their capacity. If the individual self of the trainer is brought to near nothingness the transmission would be the same as it is from the Master. It is the degree of nothingness that is achieved by the trainer that is the cause of different types of transmission. In our Institute every effort is made to ensure that the level of transmission is not less than that of the Brahmand even as ordained by Master in the book Reality at Dawn.
Your considering me as a brother helping in sadhana is good. But to think that I am your guru is not correct. Guru always is Rev.Babuji. If we accept someone than Him as the guide there is an inevitable tendency to form what is called a GURU PARAMPARA in Hindu tradition. It is there in other traditions also. This leads over a period of generations to dilution of the quality of the Guru himself as every successive generation of Gurus would have added their nominal identities to the Guru and the Guru himself becomes a gross entity most unintentionally. This is what has happened in other systems as you are aware of our Acharyas of different sects.
Pranahuti is an act of Will supported by the Divine will (because of the connection the trainer has got with the Master specifically for this purpose). Receiving grace is a different matter altogether. The Master has defined Grace as the sweetness of heart of God and I like this definition much. What love Divine has for us only those who enjoy can appreciate!
The sacred waves of the Ocean of Bliss that we experience is due to the cleaning method advocated by the system. This is in fact our own will that is taking this shape. If we however convert the evening cleaning method as prayer this attitude of thinking that the waves are coming to us from Master gets accommodated and the effectiveness of cleaning itself gets affected. Cleaning is always an act of Will on our part. The suggestions have to be clearly understood.