What is the role of a chemical engineer in the oil industry?

Chemical engineers design chemical plant. So for example in the oil industry they may need a distillation column. The chemical engineer will calculate the size required, the diameters of pipework, size of pump, energy supply, coolant supply etc. Or maybe a particular part of the plant is not of sufficient capacity. Chem Engineers will investigate the plant to improve throughput. "De-bottlenecking" is a big part of the job.
Chemical engineers are reasonably well paid but like most professions you go in with a degree at the bottom of the heap because ALL the Chemical Engineers will have degrees. You will start doing all the mundane stuff building your experiience and expertise as you go.
If you want to be a hands on Chem Eng then a degree will do. A PhD would not get you very far unless you want to specialise in research rather than hands-on.

For the chemical engineers , there is 3 positions you might work in oil industries.

First, operation which is the most common, you will wear the coverall and work outdoor or sit in front of the panel to check any problems and at the end you will be in-charge for the whole process and decide what to do to solve problems (ex. Dec furnace temp) . This may be not true chemical engineering job but as there are so many ChE some must do that.

Second, design is to work on new designs for plants or units , you may modify a unit or be a part of group making design for expansions. This is the main ChE in which you can employ everything you learnt.
Finally, to work in construction , giving instructions as expecting problems (near to design)
you've to know that you won't graduate and suddenly become the well paid engineer who has a perfect job.

A college degree is enough you don't need masters to work in an industry as a chemical engineer only further studies for researches