Does the P320 use the same sight tool as the other Classic pistols like the 226 & 229?
Specifically this one:
Sight Adjustment Tool : SIG SAUER SIGHT ADJUSTMENT TOOL | Brownells
Also, do the sights remove L-R or R-L?
No that one will not work, the 250/320 series and also the SigPro Series (2009/2022/2340) have different dimensioned slides, although the sights themselves are interchangeable.
The only one I am familiar with is the MGW Sight Pro, which requires different "shoes" for each different series of gun involved.
MGW SIGHT PRO | Brownells
Scan this Brownells listing, and you can see, that the 238, 938, also use different "shoes".
At $300 for the basic tool, it is quite an investment, but if you deal with several different brands, and even models of firearms, this could be a worthwhile investment.