I typically make my BC in advance for what i will need for the week and store in an airtight container in the refridgerator...

I tend to make mine on the medium consistency side, and really seems to stiffen up after it's cooled...

My question is what is the best way to rewhip the quantity i intend to use...? Should i remove it from the fridge and allow it to soften naturally or should i do it mechanically...? and if so, how do you approach that...?

Naturallyif you've planned ahead and have the time. Stir by hand with a spatula to remove air bubbles if necessary. I wouldn't rewhipunless it's too dry and more liquid is needed.

What kind of BC do you make? You would treat a meringue based buttercream different than an American BC..

I typically use the Wilton recipe for BC...

Okay. I can't help you there then. I use SMBC exclusively. Sorry!

Let it come to room temp. Using a small hand whip stir it in a figure '8' motion for a couple of minutes.
OR if using enough to fill your mixer bowl, let it mix on low speed (I usualy use a KA) for 2-3 minutes until it looks creamy and smooth.