Assuming the part you seek is the one in photo #4, the only way that I have found to buy that piece is part of a set like
this one. This isn't the only option out there, just the first one I could find. If you keep looking, you'll likely find a less expensive option. That said, this part is supposed to be used as part of the water return jet, not the intake. See
this illustration where your part is shown in the upper left side as part of a water return jet for the smaller Intex Easy Set pool.
That aside, there are a couple ways you can connect your intake hose to the pool.
Option #1
The intex way simply requires that you connect your hose directly to the intake sleeve and secure it with a plastic clamp that came with the pump.
Option #2
Alternatively, you could attach
a valved connector like this one to the intake sleeve on the outside of the pool, then attach the hose to the valved connector. This has the added benefit of allowing you to cut the water to the hose should you need to do some maintenance. Again, there are several versions of this connector available so shop around.
Bonus feedback - The precut hole in your reply above is the opening where a larger water return jet goes. The return jet looks
like this and typically comes with the larger Intex pools. Unlike my examples above, these parts don't leverage a pre-existing sleeve. Rather, they simply insert into the hole and leverage compression to secure the return jet to the wall of the pool.