What power supply can I use for an Auvio bts300m little red Bluetooth and mono speaker input : 5V output : 3W

At $30 it is pretty much a disposable item. It is a shame, because the reviews are good. See is you can find a local electronics hobbyist to look at it.

https://www.reallytech.net/catalog/product/view/id/11227/s/auvio-hbt2000w-home-bluetooth-speaker/

Reviews

https://www.amazon.com/AUVIO-HBT2000W-Bluetooth-Speaker-White/product-reviews/B00FP2PX28

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1. Red wire (5V): Connect the red wire from the throttle to the 5V or +5V output on your controller. This wire provides the 5-volt power supply for the throttle.
2. White wire (Output): Connect the white wire from the throttle to the throttle signal input on your controller. This wire carries the throttle position signal and communicates the speed or power level to the controller.
3. Black wire (Negative): Connect the black wire from the throttle to the negative or ground terminal on your controller. This wire completes the circuit and provides the ground connection.
4. Green wire (Battery positive): Connect the green wire from the throttle to the positive terminal of your battery. This wire provides the positive power supply for the throttle.
5. Yellow wire (Switch): The yellow wire is typically used as a switch wire for the self-lock function. Depending on your specific controller and setup, you may need to connect this wire to the designated switch input or function on your controller. Consult the documentation or instructions provided with your controller for proper connection of the switch wire.

If you have a stereo system that is in the higher bracket area then just connect your TV to the TV input jacks on the back of your amp. Or use the "Phono" input jacks. Nobody listens to vinyl anymore anyway.

Sometimes you have to enable audio outputs in the menu on the tv. Not all tv's have output for sound either. Haier is not a premium brand so don't expect to many features

Check your menu on the Samsung to switch audio out selector. You might have to use ANALOG outputs instead.
you could then eliminate digital to analog adapter.
Analog out uses the RCA PLUGS.

My Bluetooth speaker's light for the Bluetooth (middle light) blinks rapidly, alternating blue and red. Any ideas?

How can I pair an auvio pbt500 speaker to my pc?

Acquire a replacement power cable simialr to the one missplaced.

Your subwoofer probably has both high-power inputs and "normal"low inputs. The first are for receivers, which don't have link-level output for sub, so they are able to take already amplified signal as input.
You need to use link-level input of your sub and connect it to subwoofer-output of your receiver. The output is marked as OUTPUT - Subwoofer and is black-color RCA plug (don't confuse with subwoofer INPUT under MULTI CH INPUT).
Receiver has only mono output for subwoofer. If your sub has stereo input (white/red RCA plugs), connect just the left channel to the receiver, it will still work.
Don't connect anything to the speaker output on the sub, you don't need that.

I know this is a little late but I have one and the hookup is very easy, On the right side of the amp there is a six pin plug. Above it it says BATT REMOTE GND. The two pins below BATT are the battery (V+). The pin below REMOTE is the (V+) switched turn on. The two pins below GND are the ground. The rest is simple. Two RCA inputs. The switch to select MONO(R), STEREO, or MONO(L) works as explained. If you want stereo, put the switch in the middle and supply two inputs and two speakers. The MONO(R) and MONO(L) are to select a single input that will supply a single (bridged) output. Connect two speakers and they will supply the same source or connect one speaker to the outer speaker terminals for higher power output. The variable or fixed switch just bypasses the GAIN CONTROL knobs(used for Alpine's 8 pin DIN plug on unit, for older EQ's and head units.