What expenses did a village have?

None. Villages didn’t have incomes or expenses. They didn’t have mayors either.

The mayor means that this is a city with ancient rights, for such a city see my answer: How did cities operate in medieval times?

Let’s assume you just meant that the peasant with the largest share right to strip farming is willing to die to suggest something to the lord of the manor?

The village has no income. The common fields of the village are allocated in shares of land divided up as strips. The strips are distributed by ballot and someone with two strips worth of shares might be allocated strips for that year at the opposite sides of the village’s surrounding arable land. Each strip is owned but with the open fields and limited tools people work side by side in major tasks.

Peasants with little or no land hire themselves as labour to their neighbours for beer, food and account. The account money is generally for paying extractions, or taxes. (Cf Dave Graeber here). Serfs with no land are either supplied food and beer, or have to steal time from their owner to work their right or partial right to the commons. Slaves don’t even have access to this common right (yes there were slaves in England.). The excess product of the village is converted into beer, stores, or meat by feeding. A significant amount is extracted directly as rent, tax or tithe (Church tax). A very small number of people will be free alloders who own their land outright and are full free men not required to supply labour to a lord and master.

The lord of the manor will either rent his land, or use his rights to demand free labour from his peasants, or he shall do both. This is how he extracts surplus product: as crops by rent or labour. He may also use invented rights to make onerous taxes such as destroying all hand mills and ovens and forcing his peasant and serfs to use his mill and his oven. This also extracts account money from the villagers.

Where the village lays on the scale of alloders to slaves, where the rent taxes and tithes lay of the scale of nominal to crushing, these depend on the local history of class conflict. Whether surplus is extracted in kind, or through account money and forced “sales” of animals or other moveable goods depends on economic density.

Given that your village is on reclaimed “desert” (forest / waste) it may be an illegal settlement on Kings land and has no lord and a very equalitarian land distribution (all men equally free and equally outlaw). Then the men on horses with ropes will come and hang a significant number of leading men, rape the women, and enslave or enserf the remainder. Or the village could try to buy its way out, but this is unlikely as they don’t have luxury goods to bring to an irregular (quarterly) market. And as outlaws they’re not going to show up to a quarterly market with its courts. This is the case in an overpopulated country where most villages are full and there is great land hunger.

Or the village could be a colony, a settlement established. This is the case where there is a population lower than the arable required for working. Given the abandoned settlement this is more likely your case. The local lord has tried to get families here by boasting of low taxes and little corvee labour. (With too few peasants in general, rent won’t be an option as the economy will lack specialisation and even money of account won’t be in use.). This involves mostly middling peasants, everyone has a common right and enough strips to feed their household, nobody sells labour.

The village has no income, it consumes, stored or has its product extracted by King lord or church.

Correspondingly the village has no expenses. With small and irregular markets not only can they not market their crops, there is no marketing of goods back. Cloth and tools are hideously expensive, and probably produced from local wool hides and flax. Iron slowly percolates in as existing limited supplies wear out and locally made tools become unrepairable or unreworkable. The slow and slight leakage of crops not seized by the lord, usually as meat for the quarterly market, allows the counter flow of iron or lordly luxuries.

No money circulates in the village. Villagers use account money (remembered debts) when required and settle irregularly and after long debt exchange. The village doesn’t keep a book of accounts of collective work. The Lord demanded corvee to drain the water meadow common. The tithe includes wood hewing and timber getting and roof repair.

The only money in the village is in the pathetic church treasury for conversion to more resplendent vestiments, and in the lords strongbox from when he sold a horse to a knacker to buy a new one at a later date. He spent the cattle money on beautifully dyed tapestry thread so his women can commemorate the family name in fabric.

For sources start with the historiography section of https://en.m.wikipedia.org/wiki/Economy_of_England_in_the_Middle_Ages