So many questions; steep learning curve you know. My previous boats were a Xebec and a French Galley; no square rigs. I see in a couple of your 1:50 photos P&S bowlines coming off the fore end of the lateen mizzen yard which look like they engage the lower rear main shrouds and terminate at fife racks. Is there also a tack line(s) off the fore end of this lateen mizzen yard for down tension?
There are a couple of lines at the aft end of the lateen yard that go from its end down to the deck. In later ships an equivalent line would be called a vang, but not sure if this is the term to use on a lateen rigged yard.
There are no lines progressing up from the forward end of the lateen yard on my model for the purpose of tension.
The lateen of this period usually had a pair of tacks at the heel of the yard, which were attached with hooks to a pair of eyes or loops at the heel of the yard. These led to the sides and had to be removable in order to tack the yard around the mast. Downward pull on the heel was not used to keep the yard peaked, as it only increases the load on the halliard. Instead, it was more common to rig a topping lift from the peak up to the mizzen topmast. This assisted in peaking the yard when tacking as well as carrying some of the weight at that end of the sail. Vangs were a later addition, since the side-to-side movement of the yard was controlled by the tacks and the mizzen sheet.