I work on lawn and garden equipment, ice augers, generators and stuff. 20 something units a year. I’m retired and do it as a hobby, don’t charge anything,just for what ever parts I stick in it cost. So I’m getting busier after every one I fix! Ha. Most if not all push mowers have the gas tank above the carb and rely on gravity to fill the carb bowl. That’s why many have primer bulbs. Tilting the mower so the tank is up and draining towards the carb will help fill the bowl maybe, especially if your tank vent is obstructed or primer bulb is not working. Gas should fill the bowl regardless when you prime it. If not you likely have a needle and seat issue or venting issue or bad primer.
60 to 70 % of the motors I work on have gummed carbs and or rotted fuel lines. The other 20 - 30 % of the time it’s the magneto. Engines that have the fuel line inside the tank (most 2 cycle weed eaters, chain saws weed badgers and old two cycle ice augers) usually with a filter attached to the fuel line inside the tank rot out. They will run till the fuel gets lower than the rotted area then start sputtering, quit and then won’t start.
Never ever run alcohol gas! Put a little stabilizer or sea foam in at the end of the season, run them for 5 - 10 minutes, turn the gas off and let them run till they quit. If you don’t have a gas shutoff put one in! But not on a 2 cycle! Don’t want to run them dry. Just put stabilizer in run them for a few minutes and shut them off.
They run for years! Oh ya if a 4 stroke should adjust the valve lash about every 100 hours or so on a small engine. Seems like the bigger rider or zero turn motors you can stretch the valve lash to 150 to 200 hours. The manual will tell you.