It depends on if the carb has a round or oval bore ... Oval bore carbs are smaller in flow than their outlet bore so a "30" Mikuni for instance is actually a 26 mm carb... You add the height and width of the venturi at the slide together then divide by 2 to get the actual carb size ... Round...
That filter material on the intake will be choking the engine ... Backfiring through the carb indicates a non seating intake valve or ignition timing way out ...
You'd have to try either local pitbike dealers or try dhz.com.au ... Fast Ace and DNM used to have good forks but they're not cheap ... When asking about forks you need to know the length of yours , fork tube and triple clamp dimensions and what bearing sizes the frame takes ...
You have to visually check to make sure the choke is on or off ... I've seen a lot of cases where ppl thought the choke was on when it was off ... The first thing you should always check are the valve clearances (.003" inlet - .004" exhaust) ... A non seating inlet valve sends cylinder pressure...
If it's JASO-MA spec or non friction modified (energy efficient) it'll be OK ... It doesn't hurt to check the oil spinner and clean it if it's dirty ...
It looks like the number you're after is Colour code R-23 ... https://www.motorcyclespareparts.eu/honda-parts/honda-color-codes.aspx And ... Honda Paint Codes