Persistent problems such as hard starts when cold, lean misfires and poor performance across the throttle range are indicative of a carburetor that needs attention. The rubber components inside can fail and the ports and passages within the carburetor body can become clogged. You can solve most carburetor problems with a good cleaning and the installation of a rebuild kit.
A carburetor (American and Canadian spelling), carburator, carburettor, or carburetter (Commonwealth spelling) is a device that blends air and fuel for an internal combustion engine. It is sometimes colloquially shortened to carb in North America or carby in Australia. To carburate or carburet (and thus carburation or carburetion, respectively) is to blend the air and fuel or to equip (an engine) with a carburetor for that purpose.
Carburetors have largely been supplanted in the automotive industry by fuel injection. They are still common on small engines for lawn mowers, rototillers, and other equipment.