Sorry for late response.

Tl;dr: we don't know for sure, but I'm afraid that the communal drinking bowl was not a thing in Viking Age Scandinavia.

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[Part 1]

While I can also confirm the usage of Old Norse word skál primarily as a drinking vessel (a kind of goblet?/ sorry for the meaning is only provided in Danish) in online edition of ONP (Dictionary of Old Norse Prose), the tricky part of OP's question is the difficulty to ascertain its allegedly "communal" use in texts.

Among the listed 14 examples of the word in medieval manuscripts, probably the most telling one is the one from Skáldskaparmál section in Snorri Sturluson's Prose Edda. Once Óðinn (Odin) had competed with Hrungnir the Giant on whose horse was better, and the latter took a visit in Ásgarðr. While the gods (Æsir) invited him to drink, Hrungnir behaved arrogantly:

"And when he [Hrungnir] got to the hall-doors, Æsir invited him in for a drink. He went into the hall and demanded that he should be given a drink. Then the goblets that Thor usually drank out of were brought out, and Hrungnir drank out each one (voro þa teknar þær skalir, en Þoʀ var vanr at drekka af) (The translation is taken from: [Faulkes 1987: 77])."

The point here is that the big (probably) goblets in question were usually reserved for Þórr (Thor), not the communal drinking bowl of the gods. In other words, they didn't just pass their communal bowl to the visiting giant - at least in this case.
It is also worth noting that Hrungnir drank out several, not single, goblets one after another, as Þórr (Thor) probably made it rule to do so in the hall (otherwise, the gods didn't have to reserve several vessels for him at the same time!) Alleged smaller capacity of the vessel also suggests that it was perhaps usually frequently re-filled.

While the word skál was not directly referred, some other examples in Poetic Edda also suggest that individual participants of the feast also received the drinking vessel - often in form of drinking horn - from the serving lady.

• In The Lay of Sigrdrifa, Sigurðr (Sigurd) the Dragon-Slayer once awakened the sleeping valkyrie, Sigrdrifa and received a memorial drink (minnisveig), mead filled in the drinking horn ("She took a horn full of mead and gave him a memory-drink (Hon tóc þá horn, fult miaðar, oc gaf hánom minnisveig)." (Larrington trans. 1996: 162)
• The following long passages are excepts of Poem, named the Death of Sinfiotli (Frá dauðpa Sinfiotla) - Sinfjötli (Sinfiotli) was son of Hero Sigmund of Volsung and also half-brother of Sigurðr (see above), but Borghild, wife of Sigmund (Sinfjötli's stepmother) wished his death, since Sinfjötli had killed her own brother: "But at the funeral feast Borghild was carrying the ale around. She took poison, a great, full horn of it, and gave it to Sinfiotli. But when he looked the horn, he realized that there was poison in it and he said to Sigmund, 'This drink is cloudy, Dad!' Sigmund took the horn and drank it up. It is said that Sigmund had such a mighty constitution that no poison could harm him, neither outside or inside; and all his sons could withstand poison on their skin. Borghild brought another horn to Sinfiotli and told him to drink, and everything happened as before. And the third time she brought him a horn and offered him taunting words if he did not drink it up. He spoke to Sigmund as before. He said, 'Let your mustache strain it, son!' Sinfiotli drank it and died immediately. Sigmund carried him in his arms for a long way.......(Larrington trans. 1996: 138)."

In the latter episode, Borghild prepared at least three horns (two if she re-filled either of them in the third times) and passed the poisoned drink directly her stepson. If to pass the large communal drinking vessel one after another was an widely practiced social norm, she didn't take much care of to whom she passed the horn at first (since her husband was immune to the poison).

On the other hand, interestingly, some other examples of the use of skál are found in translated texts : To give an example, Stjórn is a collection of fragments of Old Testament in Old Norse, and its scribe employs the word skál to translate Gideon's "bowl" in Judges 6:38.

A few episodes from late 11th to 12th centuries suggest possible deviation/transition from the traditional practice of drinking horn, but the interpretation of relevant texts is not so straightforward to associate this transition with communal drinking bowl.

To give an example, The Saga of King Olav Kyrre (r. 1067-93) in Snorri's Heimskringla states:

"King Óláfr used these customs in his court, that he had his cup-bearers stand before the table and serve him in goblets (borðkerum) and likewise all the men of rank that sat at his table. He also had candle boys that held candles before his table, as many as there were men of rank sitting there. Further out from the high table, there was also a marshals’ seat, that the marshals would sit on, and other important men, and they would face in towards the high seat. King Haraldr [Sigurðarson hardråde (d. 1066), father of King Olav Kyrre] and other kings before him were accustomed to drink from animal horns and carry ale from the high seat across the fire and drink a toast to anyone he wanted to (Saga of King Olav Kyrre, Chap.3. Translation is taken from: [Finlay & Faulkes trans. 2015: 124])."

While I cannot confirm the historicity of this alleged change of drinking/ court custom during the reign of King Olav solely based on this paragraph, it can nevertheless represent a kind of gradual cultural change.

The saga also cites the poem of Stúfr ‘the Blind’ Þórðarson (Icelandic skald, born around 1025) as a testimony of previous drinking custom further :

"I knew the victory-blessed inciter of war [WARRIOR] [=King Haraldr] to welcome me with a good wind of Gríðr <giantess> [MIND]—he was the most bountiful to know—, when the feeder of the blood-starling [RAVEN > WARRIOR] [Haraldr], ferocious to rings, himself went willingly to toast me with the gilded horn at Haug (Stúfsdrápa, stanza 1. Translation is taken from Official Site of Skaldic Poetry of the Scandinavian Middle Ages).

The points of this stanza on our topic are:

• The drink horn was also actually used at the royal court of Norway at the middle of the 11th century (AFAIK this is almost only example of the use of horn as a drinking vessel in Old Norse poetry - on the other hand, 3 examples of skál are difficult to identify its meaning either as a drinking vessel or a usual vessel, aside from the distinction between personal or communal). It also means that the Vikings (at least military retinue of the ruler) probably "toasted" with the horn, not with the bowl/ goblet here.
• While the filled ingredient of the drinking horn could be shared between the ruler [King Haraldr] and the poet [Stúfr ‘the Blind’], the stanza itself does apparently not suppose the horn was shared at least also by other guests - Stúfr the poet remembers this event as a kind of special favor from the patron, Harald who handed the gilded drinking horn out to him (as the guest of the feast) in person, possibly on behalf of servant. I'm not sure whether this had actually been the norm in the 11th century, but at least this stanza say nothing about the shared, big communal drinking vessel.

Thus, I have difficulty in finding almost any concrete example of the Vikings' allegedly "communal" drinking from a single, big bowl by passing the vessel one after another participant of the feast........

[Continued to be Part 2]