How to stop a continuing slight bit of water entering the bowl. A plumber put a new unit in the tank about 3 month ago, but I do not think he put a new flapper.

conventional flush: push lever, chain lifts "flapper" over the hole to allow water to enter bowl. As water goes down in tank, flapper covers the hole to allow the tank to refill. The small tube that dumps water into the standup, larger tube is what fills the bowl back up. Otherwise it would stay in a low water position allowing sewer odors into the structure. If the water does not stop, your fill valve is not shutting off. Probably needs an adjustment. If adjustment does not fix, replay flush valve.

Seal between tank and bowl dry rotted. Should be able to find a replacement at HD or Lowes. Problem is if it's super old the bolts holding the tank to the bowl are probably rusted solid. May have to drill them out. When that happens to me I get a new unit. Wax seals are more fun than rusted bolts any day and a decent commode only cost $140.

This is diagram of a typical toilet tank setup if the refill tube is not putting water into the flush valve as pictured the toilet will do what you have described.

theres probably debrie in flush valve, mite also try putting food dye in tank (any color) if it appears in bowl the flapper is seeping water and activating flush valve..

Try replacing the flapper, they are cheap and so long as the tank and or bowl are not cracked you can replace all of the internal parts and basically have a brand new toilet much cheaper then replacing the entire unit. Go down to your local hardware store and everything you need is in one simple kit with very simple instructions. Good Luck.

it is filling up too much you can adjust the arm there is a screw on the side that adjusts the leval of water in the tank

It can be one of two things first you either have air in your watter line in this case let water run for a while and see if you get air if so let it run until it quits spitting or contact your water company for help.Second the diaphram is worn in the top of the valve in this case the whole valve will need to be replaced turn off water flush toilet put pan or bowl under water line at toilet remove water line at toilet .Unscrew the fitting and remove hose next remove the large plastic nut on the bottom of tank .Some water will leak out hence the bowl! remove valve replace wit new one line up in same direction it was removed put on new rubber washer supplied,Tighten plastic nut replace hose and tighten turn on water that should fix it!

Go to the hardware store and get a tube of plumber's grease. Then grease up the gaskets and the rubber ring. Snug everything down and if it leaks snug it down a bit more

get a new filler assembly. the water in the tank is heavy enough to close the seal completely. or the rubber seal is not making contact. thats' why the leak.
change the whole assemble ususally correct the problem.
adjuste the flow to about 1/4 to 1/3 under the over flow. if that still don't give you the pressure. you ca adjust the flow tube to 1/5 under the cover. that is the max.