The definitions you are asking for, can also be given to you, by starting to believe that "ελέησον " (eleison) exists.

Please help me in translating to Greek this name "Brotherhood of the Jesus Prayer" and please provide me with a transliteration of the Greek text in English.

Your title in Greek would be "Ἀδελφότης τῆς Προσευχῆς τοῦ Ἰησοῦ", transliterated as "Adelphotis tis Prosefhis tou Iesou".

Well, you must consider that ἐλέησόν is II person imperative, but it is an aorist, in conseguence, being an imperative, it is present time, but it means an istantaneous action, such as "have mercy of me now, in this present time and not for ever".
This is the difference between istantaneous and continuos action which is peculiar of Greek and parhaps, also of other languages.
It is difficult to find a book which explains these facts, I have on order a German grammatik of Greek which is the best modern one. For ancient Grammars I would reccomend GRAMMATICI GRAECI by Georg Olms Verlag which has a section, by an ancient grammarian, specific for verbs.

May I have your assistance once again. Please translate to Greek the following words:

a) "prayer brotherhood;"
b) "Superior (of the brotherhood);"
c) "prayer-meeting;"
d) "prayer-house."

Please provide the Greek text and an English transliteration.

Thank you very much on your kind assistance to our brotherhood; we will always include you in our prayers.