What is the source for brachos and amen parties wherein a group of people sit together and take turns making various brachot and answering amen? Do these events violate any halachot?
I've gone to two and they've been very inspiring with a lot of Torah teachings and stories of miracles. There were women of all ages and even some children from second and third grade up. We were given sheets to put the names of people who need a refuah, or assistance in any way in the different categories and told to think about them when we got up to that bracha. There is also a page of "yehi ratzons" or extended prayers to say after each of the brachas. It wasn't about eating. Most people took small amounts of food, just enough to say a bracha. It was about opening the heavens to hear our prayers and answer them. There are less foods than at a Tu Bishvat Seder or (on Rosh Hashana), and there's only one cup of "hagefen." There were women there from all different shuls, and several rebbetzins. The rebbetzin leading the evening encouraged us all to take on something extra in our observance of mitzvot. The party I was just at also gave tremendous chizuk to a young mother of six children who was just diagnosed with cancer for whom the evening was dedicated. I don't see how or why it would be construed as problematic.
The linked aticle http://www.dailyhalacha.com/m/halacha.aspx?id=2280 quotes the Ben Ish Chai as saying that brachos party are a specific merit for an ill person. It says in a very short summary that it is basically the zechus of all the brachos and of all the amens.
The simple answer is there is no explicit source and this is a new idea.
There are those who bring an idea from Dovid Hamelech about instituting 100 brachos daily. There are those who also bring the Yalkut Shimoni Yeshaya 26: Remez 429 that one amen can even save rashaim from gehenom. Reish Lakish also says that the gates of Gan Eden are opened when one answers amen with alls one might.
Rav Aviner was asked what his thoughts are on Seudas Amens. He answered that this is a new thing ,but it is permmisble to attend because nothing prohibited is being done . However, people should rely on classic rooted ideas such as teffilah,teshuva, and tzaddka. He was also asked is it kdai(worth going). He answered that it's better to stick to things which are rooted in our tradition than new ideas.
I saw that Rav Dov Lior was less empathetic and held that one should stay away from something which has no source in Chazal . He also brings the pshat of the Netziv on the words lo sassuru that it means not to make up your own way of serving HaShem ,something not in Chazal one should stay away.
From a practical standpoint, if one is not profieceint in hilchos brachos one can make brachos that are not necessary which is a prohibition.
Text of Rav Aviner:
שאלה: מה דעת הרב על "סעודת אמנים"?
תשובה: זו המצאה חדשה. מותר להשתתף, כי לא עושים שם שום דבר רע, מברכים ועונים אמן. למה נשים עושות את זה? כדי שיהיו זכויות בשביל עצמן, בשביל חולים, בשביל בנות שתתחתנה וכו'.
אבל, אם אנשים רוצים להוסיף זכויות אין צורך להמציא דרכים. תמיד הבעיה הזאת עומדת בפנינו כיצד להוסיף זכויות. כתוב: תשובה ותפילה וצדקה. צריך להתפלל, צריך לתן את הכסף של "סעודת אמנים" לצדקה וצריך לעשות תשובה על מה שאתה לא בסדר.
האם כדאי להשתתף ב"סעודת אמנים"? עדיף להוסיף זכויות לא על ידי דברים שממציאים עכשיו אלא ע"י דברים קבועים וברורים.
יש עוד צד, שזו פגישה חברתית. ישמן נשים שנחנקות בבית וצריכות לפגוש חברות. בלי לפגוש חברות הן מתות – 'חברותא או מיתותא' (תענית כג, א). במקום ללכת ולקשקש במכולת, אומרות ברכות ועונות אמן – בסדר.
אבל, ד' כבר חשב על כל זה ונתן לנו תרי"ג מצוות ולכן אין צריך להמציא כל מיני דברים