Should all four tires be from the same brand with the same tread?
I have a Dodge Challenger 2010, is it ok if I have two front tires from one brand and two rear from another?
This would only really be an issue on an AWD car. You can take several different mfg tires of the same size and measure them and there can be up to 3/4" difference in height. That's why it's best to at least keep the front or rears matching. on a AWD car you really need to keep them all matching. People that can't afford new tires and go buy used tires, I've seen them end up with four different makes of tires. And they don't understand why they eat tires so quick and have to keep buying used ones. Example, you have to use the temp spare on front wheel of an FWD vehicle. It's ok to get to a tire place. But they eat up quick when driven as a regular tire. More from the fact it's a different size on the differential than anything else. And long term it will cause wear on the differential.
should not be a problem, assuming they are the same size
can extra width cause additional wear and tear of components?
If law allows that, why not. In some countries all 4 tires have to be the same model.