Arduino Nano - How to add multiple sensors? Lithium battery requirements? LED requirements?
Warning: unexperienced experiments even with low voltage may result in dangerous situations. E.g. a typical 10 Ohm resistor on 5 V may get so hot that it starts burning. Make yourself familiar with basic electronics, ideally with the help of someone else who can explain it to you. That person should especially explain the safety instructions first.

Both need to be plugged into the &quot;5v&quot; pin but there seems to be only one.

5 Volts means that this is a voltage source. In an ideal voltage source, you can basically plug in as many components as you like.
A real world voltage source will have a power limit. So you need to find datasheets of all components: the Arduino and the sensors. You can then read how much power the Arduino can provide and you can read how much power the sensors need.
As long as the Arduino can provide more power than the sensors need, that's ok. If it can't stuff will become more complicated, since you'll need another 5 V source and find a way to connect them safely.

Is there a way I could split the pins to add multiple sensors?

One does not split pins, one connects additional wires to a pin.

Will data be taken in simultaneously, and be cross compared with each other for code execution?

The 5V pin is only a voltage source. It will not provide or receive data. You'll need another pin or even multiple other pins to send and receive data.
Sometimes you can only have one device per pin (like a digital out pin), sometimes you can have multiple devices on a few pins (like I²C, SPI, 1Wire).
Typically, you would define what you need and then buy the components so you can build it. This requires a bit of knowledge, so watch some tutorials or introduction videos first.

I dont want to use breadboaard and want to wire directly to chip.

Sorry to be that direct, but at your level of understanding, that's probably not a good idea. Build it on a breadboard first and once it works as intended, make it a soldered circuit.

I need to wire up a rechargeable lithium battery to both projects, I have a 3.7v 1000 Mah lithium battery and a charging port, but do I need more?

As you said your components need 5 V, a 3.7 V battery will not help you at all.
You also need to be careful with the terms: a Mah is something totally different than a mAh. Don't confuse other people by mixing Mega (millions) with milli (1/1000).
Other than that, again, read the data sheets, find out how much current each component needs and sum it up. Then divide the 1000 mAh by the value you found, e.g. 100 mA and you'll get 10 h. That's how long it will last. Maybe it's good for your purpose, maybe not. How should we know that?

I want to make sure it will work with just those 2 parts.

That's great. Just consider all the aspects written in the data sheets of the components and it'll be fine.

I also need to wire a multicolor LED to the board, but do I need any resistors?

Yes. Read the data sheet of the multicolor LED and build a voltage dividor according to the values you find.

Totally new to EE

That's probably true. Maybe you want to start at the beginning and not jump into such a complex project. Get some resistors, measure voltages, measure currents. Make an LED light up. Learn about Ohms law, you'll need it very often. Once you got familiar with the basic stuff, come back to this project.
Honestly, I think you'll destroy components if you start with &quot;a couple of projects&quot;.