if one injects the essential oil alone with the split mode 1/200

0.1 ul injection volume

NMR C13

50C starting temp is probably ok, but I would go down to 40. 35 is possible in most labs, 20C is a stretch without cryogenic cooling. More importantly: make sure you use a "volatiles" column such as DB-624 or VRX or equivalent from any manufacturer.

On column injector (cold injection) and low temperature for the oven will be fine to analyze aroma compounds. Use also a thick stationary phase, 1µm is a good compromise.

wait, before you inject your sample should go a derivatization using NAOH/methanol or BF3. Because you have used hexane as a solvent, volatiles are accompanied by extraction of fatty materials. So, your free fatty acids will become fattyaci methyl esters that are voltiles and can be anlyzed by GC.

For the analytical procedure I suggest to start with 40C until 250C with 2C/min to allow better separation of compounds. put the injector at 250C. As suggested earlier, put on splitless mode and you can play on acquisition to discard solvent peak.

For the column, from my experience (HP-5/HP-5MS, or DB-5or from any manufacturer are the best0, it is polydimethylsiloxane 95% with 5% phenyl so it is an apolar column with some polar attchements.

you can have a look at my papers, I guess the one with ultrasound and the other one on microwave extraction of carvone and limonene.

good luck

Undertake steam distillation and trap the very volatile components in a liquid nitrogen cold trap. Dissolve in aanalytical  grade dichloromethane, pentane or  diethylether and dry using anhydrous Na2SO4 while cooling dry ice/acetone to avoid evaporation. Undertake GC analysis setting the initial oven and injector temperatures  at 30 oC and and 120oC . Avoid hexane since its peak may mask the very volatile components. Set initial GC oven temperature at 30oC