The BT223 fit perfeclty with all 4cly gas Toyota engines there is no way your getting a B2 oil filter on a 1.3 Toyota engine. Not sure where you did the cross reference from. But here you can see it's the B33
JS Filters :: Application Cross Reference and Image for JS : Oil (Spin-on) : C110J You can use the B33 but I prefer the BT223 because it's just a little bit bigger.
Top 1 diesel oil is great for gas and diesel since it's additive package is not to aggressive with the Zinc 1200ppm is perfect. Diesel oils have higher detergents as well so they will keep your engine cleaner so you can use that in all your vehicles.
You defiantly do not want to use the 20w50 oil in your engines unless it's a older worn out diesel. If the oil is the new API SJ rated oil you don't want that stuff it's weak sauce there zinc is around 850ppm to 900ppm and Phos way down in the 600ppm range. They do put in around 40ppm moly and some boron to make up for it a little. Not really the best oil out there.
Don't know about there diesel oil I would have to dig up a spec sheet the MSDS do not state the exact formulation but a range.