Electronic – How to design a module that send photos from microcontroller to web server via wifi

The FET you link to is not suitable for your application. Taking a look at the "typical characteristics" table, we see this:

Vgs(th) is listed as between 2 and 4 volts - already it could be higher than our supply voltage, but not especially the "conditions" column on the right: the specification is given with only 250 microamps of current. Your LEDs, presumably, will draw a lot more than that.

To figure out if the FET is suitable, you need to know how much current you plan to draw, then look for the graph plotting "typical output characteristics":

Look for a line corresponding to the gate voltage you plan to use - in this case, there isn't one low enough - and look for where the curve flattens out. If that's at a current level greater than the amount of current you need to supply, you're good. Alternately, look at the "typical transfer characteristics":

This plots maximum current as a function of gate voltage, so you can trace a line from your MCU's gate voltage - 3.3 volts - to determine what the maximum current level at that gate voltage will be. Again, in this case, the plot doesn't actually go low enough to evaluate that on this particular FET.

Keep looking - there are FETs that meet your requirements - and remember that everything depends on how much current you plan to conduct.

Personally, I'd hack one of the cheap routers like the TP-Link TL-WR702N. It can run OpenWRT, and has a Serial interface to talk to your Bluetooth module. This way, you can for example create a python script which relays the data between the bluetooth module and a computer on the same network as the router via TCP sockets.

Everything is integrated, available from many places, and this popular solution is widely supported and documented pretty much everywhere on the web. Very little electronics unfortunately/fortunately (depending on what you want to learn or what your field is).

Of course, you can also do pretty much the same thing with a Raspberry PI or simular using Wifi and bluetooth dongles.