I do quite a lot of milling wood, composite woods and hardwoods. Most of the time you need not bother if you are working with mdf or an engineered one as they are perfectly flat most times. Raw unfinished wood, so band sawn or rough sawn generally yes face them either side if you are wanting clean finishes on either side. Generally when I do my hold down which I use 20mm x 50mm x 10mm aluminium bolt down clamps I milled I will mark out on my work piece the dimensions and then give myself a good 3 or 4 mm to spare. Being aluminium you can get away with the odd scrape instead of steel where you get no chance of getting away with such. My clamps are all sorts of shapes on the tips

Be it a messy setup, it works flawlessly so i never changed it. Click image for larger version. 

Name:	20200612_125815.jpg 
Views:	244 
Size:	319.0 KB 
ID:	28417

Regards to the last cutting, I tend to leave that specific task for the cutting of the very final edge before it would disconnect from the main body that is clamped down. Ensure you have triangular tabs. Most times with wood I'll let it drop down to the bed once its been cut free as there is normally sawdust within the slot which acts as quite a good temporary restriction to stop it moving sideways.