What were the duties of British Non-Commissioned Officers during the late 18th century and how long would it take to be promoted? Also, what were relations between them and the lower ranks like?
I hit on a couple of your questions here a month ago.
The relations between the NCOs and enlisted ranks remained hierarchical. Even with in the NCOs, the rank of sergeant and corporal had some degrees of separation. John Williamson wanted sergeants to be among themselves and the corporals likewise. This was to ensure command structure among the enlisted ranks.
To be a NCO, a soldier had to have: experience, can read and write, show mastery of the drill, and capability of command. While a NCO could not command a company, they did however command a platoon or squad in the case of a corporal. The army itself did not have an established time requirement to become one. In the case of corporal, besides a vacancy, one had to have the most experience and proof of drill mastery. For the most part, it would be at least a year before any chance of promotions. For sergeant, one had to be the most senior corporal in the company or regiment. Each company had three corporals and two sergeants. That means with ten companies, thirty corporals and twenty sergeants including the sergeant major. However, seniority did not always mean automatic promotion. The Coldstream Guards put a three month probation on corporals to prove themselves, otherwise the next corporal would get his chance at sergeant. Commanding officers, such as captains, would be the deciding factor of finalizing the promotion.
However, from the standing orders of the Dragoons in 1755, they required that dragoons have four years of experience before being eligible to be corporal, and then three as such for eligibility for sergeant. So far, I have not seen other units employ the same year requirements, but still have moved to ensure competence of the prospective NCO.
Lance ranks did exist in the very later parts of the eighteenth century. Lance meaning it was not an official capacity but the soldier would act in the parts. A Lance corporal would technically be a private who had gotten the privilege to stand in as a corporal and have the same duties. However, it could be taken away at will versus a bona fide NCO would have to face a court martial before being officially demoted. These would be temporary ranks and did not increase the soldier's pay for being a lance NCO.