Espruino MDBT42Q Breakout for 1kHz Signal Acquisition

Hi,

Sample transmission and receive at at least 2 kHz

You're correct in that you can only get a max packet rate of 125Hz. This is a limitation of Bluetooth (7.5ms connection interval). However you can send a bunch of of data within that packet, and with up to date firmware 2000 bytes/second should be pretty attainable.

You should be able to use the Waveform class to sample data at 2kHz: https://www.espruino.com/Waveform

A module compact in size which can be fitted in a rectangular space of 18 mm x 30 mm.

The breakout board is about 18x28mm, but you could potentially use the module directly if you're able to design your own PCB

I found out that the device can programmed wirelessly using a Web IDE provided we have a compatible in built Bluetooth module and Web Bluetooth. Have I understood that correctly?

That's correct, yes.

Hope that helps!