How likely is it that I have insulin resistance, if my random blood glucose levels are normal?

Varies. The answer depends on many things, including what risk factors you currently have (obesity, metabolic syndrome, family history of diabetes...) just because you have a normal random blood sugar does not rule out Insulin resistance. Your body might keep your bs normal at the expense of very high level of Insulin in early diabetes. You need to measure glucose, Insulin and c-peptide level as a start.
Posxsible. It is possible that if your Insulin resistance is in an early stage your body can produce enough Insulin to give you normal blood sugars. This situatioin can be worked out by blood tests ordered by your doctor.