In the numbered parts (which I've highlighted) of the probate for Joseph Eayers pictured below:
Does that mean Joseph was a widow? And what does the "third" and "excepted" part mean?
Does "incapable of a division" mean there was dispute/fighting over splitting the will? The signing of this in 1799 was a year after Josephs death in 1798 so this may explain the year long gap. If not, how long would it take for wills have been processed in early America?
There was thought Joseph (Sr.) had a son named Joseph (Jr.) as well. In this instance, is the will referring to dead Joseph Sr. or alive son Joseph Jr.? And if its the son Jr, is he the one that pays out his father inheritance to his sibling "co-heirs"?
The "widow's third" was a portion of a man's estate guaranteed to his wife after his death, regardless of what his will stated. This excerpt from "Material Culture in America: Understanding Everyday Life" (Google Books Link) describes the concept:
Known also as the "widow's portion" or "widow's third", a widow's right of dower was ... a legal practice in ... the United States into the first half of the Nineteenth Century. A husband could will to his wife any or all of his estate. A widow could invoke her right of dower to contest a will. If a husband died intestate (without a will), however, dower right guaranteed a woman financial support for herself and her minor children. This legal practice allowed a widow the uncontested right to one-third of her deceased husband's real property held during their marriage if there were children"
So my reading of that part is that Eayers' estate was reviewed after his widow's one-third portion had been allocated to her ("excepted" from the rest), with a view to dividing the remainder between their children.
The document states that the committee
"described the _________ these so being hers, to be incapable of a division, without great prejudice to or spoiling the whole"
Unfortunately, the relevant context appears to be in the missing underscored region - we don't know exactly what and who 'these' and 'hers' refer to (although the latter is probably Eayers' widow). But the following text refers to 'these premises', so I think this is a statement that the real estate left by Eayers, the 'premises', could not easily be divided or split without diminishing their value, so they were kept as a whole. Joseph Eayers, the eldest son, would keep that estate, and pay or securitise a share of the value to his co-heirs.
Yes, this part suggests that the eldest son of the deceased Joseph Eayers was also called Joseph Eayers, and as noted above he was responsible for sharing the inheritance with the other listed heirs.
It may be worth noting that this document is not actually a will. It's a probate document, which describes the distribution of estate according to a will, if there was one. Probate can take a while, if there are complexities such as division of real estate, which may explain the delay you mention. It's not clear from this if Eayers left a will or not, but I would guess that he did not, hence the allocation of the "widow's third" and calculated distribution among the children.