The F205 (and others with OTG controller, ie 405) have internal pullups, no external ones needed.
The series termination resistors on data lines should afaik be 0-ohm. On some microcontrollers, the impedance of the internal drivers are too low and external resistors are needed. Even if it is not the case, the 0-ohm resistors are still drawn in to be able to replace them with another value in case certification fails (they cost almost nothing, but the re-design would cost a lot).
There is an application note about the internal bootloader, AN2606. The appnote says that the F2xx has two bootloader versions, the earlier one does not support DFU. Check that the chips you got are not from some old leftover stock somewhere and do not have revision B marked on them.
That appnote specifies the exact requirements for the DFU bootloader. First, check the activation sequence to be sure that no other bootloader would activate first (as only one can be active). Then make sure that the DFU bootloader does activate. The USB bootloader does not need much from the controller. Use a scope to verify that the oscillator is running (AN states it must be multiple of 1 MHz between 4-26). Measure voltages and reset line.
Although it would be possible to develop without a debugger, you should get one and use that for your daily development. The ST-Link is cheap and works well, software is free. Do your daily work with the debugger and use the DFU only for factory programming or limited field update functionality if it fits for you.
Also, beware that the DFU ST has implemented, is actually not DFU-compatible. They implemented a custom DFUSE protocol on top of DFU and standard DFU tools do not work.