Is ibn Abbas statement and statement of Hasan Al basri authentic

Question

On tafsir of verse of quran 4:34 and Muslim, 1218. ‘Ata said: I said to Ibn `Abbas, what is the kind of hitting that is not harsh? He said, Hitting with a siwak and the like" And Al-Hasan al-Basri said: “This means that it should not cause pain.” Are these hadith authentically attributed to them. Can you please provide a reference that is authentic

Answer 1

The source of such a report is clear it comes from a tafsir like tafsir at-Tabari.

Sources of the report of ibn 'Abbas's explanation

So imam at-Tabari when explaining the part:

...strike them...

from the verse 4:34 mentioned several reports that say don't hit them harsh among them is the one you've mentioned, here's the full quote as is in his tafsir (see here and the following page):
^{In the following I'm translating from Arabic language as these translations are of my own take them carefully!}

٩٣٨٦ - حدثنا المثنى قال، حدثنا إسحاق قال، حدثنا ابن عيينة، عن ابن جريج، عن عطاء قال: قلت لابن عباس: ما الضرب غير المبرح؟ قال: السواك وشبهه، يضربها به.
9386 - Al-Muthanna informed us from Ishaaq from ibn 'Uyaynah from ibn Jaraij from 'Ata who said: I said to Ibn 'Abbas, what is the kind of hitting that is not harsh? He said, "Hitting with a siwak and the like"
٩٣٨٧ - حدثنا إبراهيم بن سعيد الجوهري قال، حدثنا ابن عيينة، عن ابن جريج، عن عطاء قال، قلت لابن عباس: ما الضرب غير المبرح؟ قال: بالسواك ونحوه.
9387 - Ibrahim ibn Sa'id al-Jawhari infromed us from ibn 'Uyaynah from ibn Juraij from 'ata who said I said to ibn 'Abbas, what is the kind of hitting thatis not harsh? He said, "hitting with a siwak and alike"

Both of the above chains are connected and have narrators of a high trust level therefore it is safe to say that these reports are sahih.

He also added a third report with the same meaning(same source see here):

٩٣٨٨ - حدثنا المثنى قال، حدثنا حبان بن موسى قال، أخبرنا ابن المبارك قال، أخبرنا ابن عيينة، عن ابن جريج، عن عطاء قال: قال رسول الله صلى الله عليه وسلم في خطبته:"ضربا غير مبرح"، قال: السواك ونحوه.
9388 - Al-Muthanna informed us from Hibban ibn Musa from ibn al-Mubarak from ibn 'Uyaynah from ibn Juraij from 'Ata' who said: The messenger of Allah Allah's prayers and blessings be upon him said in his sermon: "A hitting that is not harsh", he said: Siwak and alike

This report is referring to a part of the sermon at the farewell hajj (hajjatu al-Wada') which can be found in several sources like in Sunan ibn Majah and Jami' at-Tirmidhi etc.. Of course this hadith report is mursal (its disconnected) as 'Ata' is not a sahabi.

See here hadith #5275 (٥٢٧٥) also in the tasfir of abu Hathim ar-Razi where this was reported via Muhammad ibn Isma'il al-Ahmasi محمد بن إسماعيل الأحمسي (trustworthy and a student of Sufyan ibn 'Uyaynah), from Muhammad ibn as-Silt محمد بن الصلت (trustworthy), from سفيان بن عيينة ibn 'Uyaynah ...

Sources of the report of al-Hassan al-Basri

Again at-Tabari mentioned your quoted report in the same context as above, buit a few pages later. Here the full quote (Source see here):

٩٣٩٥ - حدثني المثنى قال، حدثنا حبان قال، حدثنا ابن المبارك قال، أخبرنا عبد الوارث بن سعيد، عن رجل، عن الحسن قال: ضربا غير مبرح، غير مؤثر.
Al-Muthana informed me from Hibban from ibn al-Mubarak from 'abd al-Warith ibn Sa'id from a man from al-Hassan who said: a hitting that is not harsh, not leaving traces ^{(also possible meaning: not force full or not pain full)}.

This report certainly has issues as we have an unknown narrator between al-Hassan (al-Basri) and 'abd al-Warith ibn Sa'id (عبد الوارث بن سعيد). Nevertheless it shows that 'abd al-Warith's honesty as he was a student of al-Hassan al-Basri he could have said that he heard his master himself, but he didn't and unfortunately he didn't know the person who reported his masters words.

Ibn abi Hatim ar-Razi also reported this in his tafsir (see here) -the translation of "غير المؤثر" here is based on the quote from OP's question, I've already mentioned possible other translations in the quote above-:

٥٢٧٤ - حدثنا أبي، ثنا أبو سلمة قال: قال حماد: فقلت لحميد: المبرح؟ قال حميد: فقلت للحسن: ما المبرح؟ قال: غير المؤثر.
5274 - My father informed me from abu Salamah from Hammad who said: I asked Humaid ^(at-Taweel): not harsh? Humaid said: I then said to al-Hassan: What does not harsh mean? He said: which doesn't cause pain.