Hello. I used desktops since my first computer, a macintosh in the early 90s. My supervisor gifted me a lenovo laptop 520 legion with full hd screen, 7th gen core i7, nvidia gtx 1060, and 16gb ram. This is my first laptop so it took a while to get used to the trackpad.
It has two flat buttons below the tracking area. I can navigate the mouse pointer on the tracking area and left click on the tracking area.
I can left click and right click on the two buttons. I can also use two fingers on the tracking area to zoom in and zoom out of a page on Firefox. This is similar to what I do on my android phone.

I have two questions:
1) Is there any way to simulate the mouse scroll wheel?
2) Why is it possible to left click on the tracking area but not right click? (for example, through some gesture)

I'll probably just buy a mouse for this thing on Monday if I don't figure this out by then.
Honestly, just buy a mouse. But, just to see what options you have available, search for touchpad options on your laptop (start and touchpad in search) and see what options you have available. I have not found a way to scroll, nor have I really looked for it, but that doesn't mean that your particular machine can't do that.

And thanks for the zoom tip--never knew nor tried it since I use an external mouse.

Edit: I have an HP laptop and can scroll but have to enable in options. It was disabled by default.
Many laptops allow you to right clicking by tapping the trackpad with 2 fingers (index finger and middle finger for example).

They also allow you to scroll by putting 2 fingers on the trackpad at the same time and moving them up or down.
In some laptops scrolling is done by touching the very right side of the trackpad with one finger and moving it up or down.
Sometimes you can search through the trackpad options and select which method of scrolling you prefer.

In some cases when these features do not work you might have touchpad (trackpad) drivers missing or wrong drivers installed. (If your laptop came with Windows it will probably have all the correct drivers)
Ok, placing two fingers allows scrolling.
I'll also buy a mouse. Trackpads have high frustration potential.
i am one of those people that actually prefer trackpads to mouse for productivity purposes.

need to scroll on a page ? two fingers sliding
need to alt - tab ? three fingers to the right or left
need to hide your desktop from people in a heartbeat ? three fingers down

The only mouse i tolerate for working are the highly customisable ones, where you can configure the extra buttons for Control-tab and alt tab, my go to was the Cyborg Rat 7, but since the drivers are not updated for Win 10, i only use it as a dumb mouse.

Also yeah, as @new_user mentioned, tap with 2 fingers for the right click.

Some laptops come with windows precision touch-pads, in which case you can have the list of gestures here :

https://support.microsoft.com/en-au/help/4027871/windows-10-touchpad-gestures
Make sure to avoid any laptop with Synaptics touchpad even if it is working in Precision mode as it still has noticeable input lag compared to a MacBook or old ps/2 synaptics.
I just bought three wired mice from doculand and a wireless microsoft mouse from a computer store. I'll use the wired ones and keep the microsoft mouse as backup.