Re: mercury 200 20 hp won't keep running
1st take that can of starter fluid... and throw it away... save it for 4 strokes... but do not use it on your 2 stroke outboard... very bad juju. The starter fluid has no lubricant in it and ether has a very different pressure curve... not at all healthy for your engine if you like your engine STOP using starter fluid. In a pinch you can soak a portion of a clean rag with gasoline and cover carb intake with it so that the air only goes through one layer of gas soaked cloth, this will act as a carb and allow a choked cold start and then progressively lean out as the gas evaporates from the cloth. It will give you a fast safer indicator on if the issue with firing is a fuel problem or not, note I said safer not safe because there is no oil to provide lube this way either.
To check for fuel pump issue you can prime with primer bulb and then gently continue squeezing the primer bulb while engine running (your the fuel pump them) if this keeps engine running then your fuel pump is definitely suspect. My personal feeling is that this motor is new to you, and has been sitting a while, I would pull the carb, disassemble it, clean it very very thoroughly, NOT use welding tip cleaners to clean jets, keep the carb cleaner away from the plastic or cork parts (use dawn dish soap for them). Once you are very sure every lil part of the carb is clean, and all the passageways and holes are clean (I use hot tap water for this part as it gives me a visual that there is flow through the ports)... gently dry with compressed air and make sure you didn't leave water in there, reassemble with appropriate gaskets (new is strongly preferred but when in a hurry at the lake I have gotten away with reusing old gaskets but not recommended). Remount carb/fuel pump, connect fuel lines, prime with cover off to check for leaks, then set idle mixture screw to a richer then expected setting and proceed to start, then set for optimum operation and 1/8 to 1/4 turn richer than optimum.
I know it is a bit of work but this will get results. if you have other fuel issues.... after this, check for air bubbles in line via clear vinyl tubing replacing line to fuel pump. put proper fuel line back after you know there are no air bubbles. Speaking of fuel tubing, while you have carb off and out, replace the fuel tubing with new nifty alcohol resistant fuel tubing as the old stuff will cause you issues and plug up you nice shiny clean carb.
Sean