H-Bridge Sensing Voltage

The BTS50055 is not good for fast PWM. If you look at the data sheet in particular "load switching capabilities and characteristics" on page 3 it tells you how fast the device can switch. Turn on time is somewhere in the 100us range typically and turn off might be about 60us. These numbers need to be 1% or less for decent efficiency and 100us represents 1% of 100Hz. If your switching speed is pretty low then use it.

How can I design a MOSFET H-bridge motor driver controlling only 1 PWM for a motor?

If I understand correctly you have a single PWM signal and you want to drive a H bridge with this signal. I'd start by looking for a couple of beafy N channel mosfets like the IRF1010 and then pick a topside/lowside mosfet driver like LTC4444. Feed PWM to the inputs via a couple of logic gates that create a deadband (so both FETs never switch on at once) and this gives you a half H bridge.

Repeat to make the other half but remember to invert the PWM signal. I'd look to be monitoring current on the dc side of things and forget about the BTS50055.

Your analysis appears to be correct. Tying the IRS2003 inputs together and driving them with a single PWM signal should provide similar functionality to the IRS2004 single input device, per the hyperlinked datasheets.

The discrete inputs on the IRS2003 gives you the flexibility to manually adjust the deadtimes higher than what's provided by the IC itself, and give you complete phase control over the outputs.