Using BT module

Hello! I have bought this one:

http://www.ebay.com/itm/ws/eBayISAPI.dll?ViewItem&item=261024357609&ssPageName=ADME:L:OU:US:1123

My question is this:

1)Can ot work stand-alone, without arduino uno for example? What I really want is this: send a specific data (either H or L or a single byte) to the device that the BT module is being synced with. If I build my own board that provides the Tx pin with the data that I want to send, will the be transmitted to the device or not?

2)If yes, what type of input data does the Tx pin gets?Is it a pulse, is it a single bit, a byte or what? I cannot find it anywhere..

It is not clear which chip is on your board, but that board for sure may work without Arduino uC .
How ever it is TTL I/O so you will need some voltage pump (max323) to work like normal RS232 interface (12V).

Interface expect normal serial input on 9600,N,8 rate, and you may send any type of data.

1)Can ot work stand-alone, without arduino uno for example?

No. You need something else (a programmable microcontroller) that tells the BT module what data to send.

So what do you suggest me to do. I want something much cheaper that an arduino because only thing I want to send is only one byte, not even receive data.

To keep things simple, you can make an Arduino-compatible for $6 or less (ATmega328, crystal, a few capacitors, header(s), protoboard).
Or could use the smaller and cheaper ATtiny85.