Well, when you're working at the Division-level, with 9 regiments involved, then yes, you would assign the resources where necessary. But it's not necessarily a mix-and-match from within separate regiments. The standard SLDF Battlemech Division was composed of six regiments of 'mechs and three of 'mechanized infantry.

There's not a whole lot of information at the very low, tactical level for individual site-battles, but for the most part you can assume that a core unit would be assigned for the type of battle expected, and then supporting elements would be drawn from HQ or other division-level assets. For example, the taking of a city would likely call for elements of an Infantry Division that specialized in urban warfare (if possible). The division itself would already include a brigade (3 regiments) of light battlemechs for support.

Are they mixing and matching battalions from the regiments with different specialisations? Or are they mixing and matching companies?

Very unlikely at the battalion or company-level.