Bucklers certainly were popular in warfare all be it a bit later than the period Battle Brothers takes its inspiration from.
Hmm, I`m not so sure about that. They certainly were very popular by XIV century (as example, look here: http://www.thearma.org/Manuals/i33/i33.htm – this is early XIV century), and certainly earlier as well – there are many depictions of sword and bucklers from XIII century and XII century. If I judge by the weapons and armors in the game, the historical scope is somewhere from XI to probably very early XIV century (or more probably very late XIII century), because there are types of armor, that are from that period (1250-1300). So I think it is safe to say, that sword and bucklers were very popular in the historical period the game is based upon.
Here are collected several depictions from XIII-XIV century: https://signoresimone.wordpress.com/2014/10/29/gallery-bucklers/
I think that in the period of the game bucklers were predominantly wooden, with metal boss in center, but in later period (probably from late XIV and XV century) more popular were designs entirely made from metal. But if there have to be some progression in the bucklers, maybe there is place for one or two “later” types – one round all-metal and one diamond or irregular shaped (like this: http://www.der-schirrmeister.de/picture/B-W-001.jpg )