I thought it would be possible to programm the OSD when everything is mounted and soldered. But all i get in the GUI is: waiting OSD...
I have temporarily disconnected TX and RX at the FC, but nothing changed. 
Does anyone have an idea how i can flash the OSD without desoldering it?

you will need to at least unsolder TX/RX... i guess your OSD 5V is connected to the FC? which means when the OSD is powered on your FC is also on so TX/RX will be connected...

I have disconnected the FC, so it's not powered through the OSD and i also unsoldered TX/RX.
When I want to flash the OSD I get this error: avrdude: stk500_getsync(): not in sync: resp=0x00. (BTW, before I started the build, I flashed MWOSD 1.5 without any problems)
I just ordered the LemonCore PRO PDB (integrated OSD, I hope it's a good choice). I somehow hate this little OSD and all the wiring it needs

might sound silly... but have you tried

1. are you connecting the DTR pin?
2. tried swap TX/RX?
3. restart your computer

Yes DTR pin is connected (not sure if this is necessary), haven't swapped TX/RX and yes I even used a different computer. The initial flash of MWOSD 1.5 and configuration in the GUI at the beginning of building the quad was super easy... I have no clue whats wrong. Never mind, Oscar, I appreciate your help! I'm just waiting for the lemoncore and get rid of the minim. Voltage, current, mAh reading and a timer is exactly what I need.