Hi there PrincessJamJam, and welcome to the forum, by the sound of it you have a 160cc powertorque engine, but the following steps are also applicable to the earlier full crank engines. It would appear there is an air leak somewhere, hence it revving its head off from startup. You mentioned the carby is loose on the manifoldso i think that would be where we should start. There are 2 orings on the manifold, one between the carby and manifold and a smaller one between the manifold and the block. There should also be a wavy washer on the manifold that the carby pushes up against when it's locked in place; it's purpose is to apply some backward pressure on the carby to prevent it from loosening itself off. Check these orings are present and intact and the wavy washer is also there. Also ensure that the 2 small phillips head bolts that hold the manifold to the block are firm.
Next, make sure the hose that comes off the diaphragm housing is connected on the block end also.
(Applicable to powertorque engine only) There is also a large oring that sits under the starter housing, take the 3 bolts off and check that oring is not pinched, broken or missing. Reassemble the lot and pray for the best!
Let us know how you go and dont hesitate to ask any questions.