Firstly, don't throw the old carb away. I presume this is for a 16hp K341 or Magnum?. The Carb in your pic looks aftermarket. The original was either a Kohler with #30 in raised letters in the casting above the venturi aperture when looking through past the Choke plate. Or it is/was a Walbro. Both have different settings and the later ones from the 80s had fixed Main/High speed needle jets.
I have no experience with those Chinese Knockoffs, but have heard different opinions and experiences. Is that Carb specifically for a 16hp? or a generic one which states it fits all?.
If the Needles actually adjust the mixtures, then the top one is the high speed/main, the angled side needle is the Idle mixture. Top screw is the Idle Speed adjuster.
Need to know what your engine model, spec and serial number is to establish correct needle settings.
Will probably need to guess or take an average of the preliminary settings for a chinese one.
As for the Head Gasket, the quoted genuine Kohler ones are preferable, as they still have the folded over edges that are exposed to combustion forces.
Aftermarket ones are likely to be just a pressed sandwich style, unless you can see what you are buying. I which case, they will work ok.
Flatness of the head/cylinder faces are essential. you can check the head flatness after a clean on a good sheet of thick plate glass (smooth and very flat) and feeler gauges.
You should not be able to get a 3 thousandth (0.003") of an inch feeler gauge between the 2 faces anywhere around it. If can-.......
obtain 2 new sheets of non-creased Wet or Dry P400/P600 (1 of each). Proceed to flat the head gasket face down on the P400 (dry) in circular movements until the high/low merge.
Finish on the P600 the same way. The small impressions left by the original gasket do not really need to be removed, just aim for a smooth clean area all around.
Head bolts are torqued to 28-30 lbs ft and rechecked after an hours running.
Once the head leaks are sorted, you can sort the carb. Good luck
Edit -Bit slow, Reiver beat me to it.