I'm very new to arduino modules and working on a project. I hired a freelancer to help, but I've been somewhat left in the dark. I've been reading up on breadboards, but I was wondering if it was possible to connect these without one.
Yes, but a breadboard is a very good place to start when you are experimenting. Buy one or more.
That big one, is that a NodeMCU board? If so that's a standalone microcontroller, like Arduino but then on steroids and with built-in WiFi.
The shown receiver is a very cheap version, for better results you should use something like this RXB6 module.
which has hardware support for this kind of communication, two cores, multitasking, WiFi, Bluetooth, …
and it can be programmed in the Arduino IDE.
I would not use an additional Arduino despite interfacing to some 5V peripherals or the like.
ESP32's software support is probably not yet really matured; and if the ESP8266 is anything to go by there's little hope for support (or even detailed data sheets) from the manufacturer.
wvmarle: ESP32's software support is probably not yet really matured;
Is that your personal experience, or an anticipation?
If the latter, you should try them.
Got the module, haven't tried it much yet as I don't have a project for it - that's what I've been reading on the forums about it. Hope it's improving fast, maybe it's there by now.
The mentioned RMT module works very well driving any kind of programmable LEDs, like WS28B12, APA, …
I got some new programmable RGBW LEDs, the RMT drives them happily
and it does not have to disable any interrupts while doing so, because its done in hardware.
Buying a bunch of jumper cables should get you going. But on the other hand, why don't buy a good breadbord for prototyping while you buy the jumper cables.