"If there's no Hadran there's no meat"?

Question

I happened to observe a Facebook conversation regarding an upcoming Siyum, ostensibly taking place because someone had put forth great effort to complete a tractate of Talmud, and not because the organizers wanted to eat meat during the Nine Days. The question was asked whether meat would be served, and someone said, "If there's no Hadran there's no meat."

• Is that correct? That is, does eating meat at a Siyum during the Nine Days require a Hadran?

Furthermore, I wonder:

• Does Hadran require a minyan (the Siyum-maker apparently assumed so, and was not planning to say the Hadran)? Does the presence of a Minyan obligate a Hadran?
• Does the presence of a Minyan (with or without a Hadran) obligate a Kaddish?
• Do Kaddish and Hadran obligate one another (ie., do you need to do both)?
• And what if there's no Minyan available? Can meat be eaten at such a Siyum during the Nine Days anyway? Can someone make a Siyum with (or even without) a friend or two and then eat meat as part of a Se'udath Mitzvah?

Answer 1

R' Yaakov Shechter maintains that while it is very nice to have a minyan, it is not a necessity, and a Siyum is considered a 'Sedudas Mitzva' irrespective as to how many are present.

כל ענין המניין הוא רק לחבב המצוה ולעשות את הסעודה לגומרה של תורה ברוב עם, אבל השמחה היא בעצם הסיום וראוי לערוך על כך סעודה גם בינו לבין עצמו ודינה כסעודת מצוה לכל דבר וענין. בדיוק כמו סעודת שבת וחג שאדם אוכלה לבדו, אין היא פחות סעודת מצוה מאדם שזוכה לאכול את סעודות השבת ברוב עם.

The poskim do say that one may only make a siyum during the 9 Days on finishing something 'proper' - i.e. something that would require a Gadran. Sorry no sources off hand..

Answer 2

In the back of each Artscroll volume of the Talmud, the Hadran is prefaced by the following:

Upon the completion of the study of an entire tractate, a festive meal...should be eaten - preferably with a minyan in attendance. The following prayers of thanksgiving are recited by those who have completed the learning.

The implication is that that a minyan is not required for the Hadran.

Kaddish can not be recited without a minyan. (ibid.)

The book Guidelines for Pesach says that, in order to permit a firstborn to break his fast on Erev Pesach, the siyum must be on one of the following:

1. A tractate of Gemarah
2. An order of Mishnah
3. Any of the 24 books of Tanach, when studied in depth
4. Any of the four sections of Shulchan Aruch

Presumably, the same would apply to eating meat on the nine days. Hence, it is possible to have a qualifying siyum without having a Hadran (since the Hadran is not said on a book of Tanach or section of Shulchan Orech, as far as I know).