(Check again if your lab has not a Schlenk line or if one may be purchased, manufactured (your local glass blower), acquired (ebay-like second hand), or shared with your befriended group across the aisle. Because it is a tool equally used in inorganic chemistry, catalysis, etc. Then read a guide like this one to have some general idea, and get an instruction in person by an chemist more experienced with the design you will work with.)
The video omits one approach consisting of mounting the air dry glass ware in first place, to thoroughly dry the setup with a heat gun (a powerful hair dryer), and to allow the setup to cool to room temperature while being purged by inert gas. The drying is more efficient if the setup is evacuated and if proceeding from the inlet of the inert gas to the venting outlet. If the setup includes a condenser, then no water is allowed in the coil of the condenser during the drying. If you have the option, argon may create a blanket on top of your reaction (thus, you may save some volume of inert gas), while the cheaper nitrogen by relative density goes off to the exhaust. Note, nitrogen equally may react with some metals (e.g., Li, Mg).
After this to your questions:
He briefly closes one branch of the T either with a stopper, or rubber bulb. Don't use the Peleus sphere shown on the left hand side. The oil in the bubbler is a visual for the pressure inside the setup, and a safety valve should the pressure in the setup increase too much.
The left-hand side of the adapter shown by you looks more like a silicon tubing, than glass. Look for a thermometer adapter / inlet like the following:
(adapted from here)
Below the cap you find an o-ring. With loosened cap, push the Pasteur pipette through, then tight the cap gently and mount the adapter. But in many cases, a normal knee-shaped adapter may work fine to connect your setup with the inert gas, too.
One word: scale. Except if you really need to work at low concentrations (say below $\approx \pu{1 mol/L}$), use a smaller flask. For safety (e.g., sudden evolution of gas, foam) and comfort (intentional quench of the reaction, start of workup), it is nice to use about 40% of the flask's volume by the volume of reaction. Thus, consider a smaller flask e.g., $\pu{25 mL}$. This equally reduces the space needed in the hood, eases drying the setup, monitoring temperature, etc.
If there is no flow indicator for the inert gas, connect a hose with the inert gas supply and a Pasteur pipette and set up once a pneumatic trough. This gives you an estimate how much time is needed to replace x-amount of gas in the setup if no vacuum was applied earlier. If you evacuated the setup (pump-thaw cycles, requires gentle greasing the joints), then the bubbler indicates when you reached normal pressure in the setup.
I can not recommend this change of the setup. Mounting the inert inlet on one wing of the T, across the exhaust, no longer guarantees protection by the inert gas. Instead, it will flow the path of least resistance regardless what happens below the reflux condenser and round bottom flask.
Instead, 1) keep the inlet remote from the exhaust of the setup, 2) maintain a very low but steady flow rate to prevent air and humidity from entering the reaction flask. If you don't aim to distill-off solvent (especially at reduced pressure), then you don't constantly blow nitrogen / argon into your reaction (it is not a fish tank). You do not want to waste of inert gas, nor evaporate your solvent of reaction during the reaction.
