The colony of Virginia had a legislature, the Old Virginia General Assembly. It is bicameral, containing Council of State (Upper-house) and House of Burgesses (Lower-house). I just want to know about their term limits. How many years are in a term limit for each house.
Multiple websites have infos on its origin, but nothing about its term years or the nature of appointment/election
As a point of technicality, term length is the tenure of a single term. Term limit refers specifically to the amount of consecutive terms one may serve and the Burgesses had no such limit. They didn't have term lengths, either.
Term length was not defined the way we think of it today. Generally speaking you were elected to serve that body until a factor required another election. Some of these were automatic; the death of the monarch or arrival of a new governor would trigger a colony wide election, for instance. The death of the delegate would likewise trigger an election for his replacement. At times the governor would prorogue (dismiss) the assembly without such an event happening, which would trigger a new election, though this happened essentially at his discretion and was used to subvert their authority. An example is Gov Faquier proroguing the Burgesses in 1765 immediately before they were to vote on sending representatives to the Stamp Tax Congress, preventing their ability to do so. Nearly a decade later in response to a session dealing with the Intolerable Acts and blockade of Boston, Lord Dunmore did the same. This time the delegates marched straight to the Apollo Room in a local tavern, reassembled, and passed the boycott of British goods, anyway. An hour later a sack of feathers hung over a barrel of tar on Duke of Glouchester Street in Williamsburg as a signal to any who dare break the embargo.
The houses were split in 1643. In 1661 an election took place and the governor did not end their session until 1676, a full 15 years later. County elections happened to replace those who died or resigned, but for 15 years there was not a colony wide election. But it happened more frequently than that except that one time; that's the longest cycle between colony wide elections in Virginia's history. If you'll remember, another big thing happened in 1676 Virginia: Bacon's Rebellion. Part of the reason for that was a result of the extreme elitism of the colony under the long council, which issued heavy taxes and offered little representation. They also tightened who could vote for the common house elections during their session.
In the 18th century and as a result of the Glorious Revolution in the 1680s (and things following like the English Bill of Rights), English law had evolved to say elections should take place every 7 years, so by that time a maximum duration between elections was recognized by Virginia and the closest thing to a set term length the Burgesses ever had was established.
When an election was triggered the governor would notify the county sheriff who would then post the election date publicly for all to see in advance. On the day of the election all eligible voters (which varied as to who that was, becoming more restrictive until 1723 when the strict requirements we think of were solidified) met at the courthouse and verbally declared their vote to be recorded. It was a big event and many people came to watch the votes be cast. The sheriff could leave the poll open for several days or could close it after a clear election. Sometimes this was used for shenanigans of ensuring your candidate won, and the land holding requirement of 100 acres actually comes from a sheriff buying land in an adjoining county to vote in that election as well, since you could vote in every county in which you owned land. These weren't the only shenanigans - candidates often offered copious amounts of food and beverage on election day, adding to the party theme. Among the beverages, of course, was ample spirits and some elections were closed because the crowd simply became too rowdy from the intoxicated agitators. Elections in colonial Virginia were definitely an interesting thing and very different from our own.