In my opinion (having just done FAA CPL/IR on top of my existing EASA CPL so reasonably up to speed on the regs at the moment)...
- All the hours in anything but gliders (or any flexwing time you might have) count as hours, both dual, and solo. To the Americans, European 3-axis microlights are just aeroplanes.
- Any cross countries will count, but solo means solo - FAA requirements for solo time really do mean that. Flying as a qualified pilot with a pax does not (nor in my case, requiring me to repeat a flight in the USA, does flying as an instructor with a student).
- Check really carefully FAA requirements also for cross country distances and ensure that you can prove you meet them.
Your sub-ICAO licences, on the other hand are worthless in the USA.
So, I think you'll be doing instruction as required, the FAA PPL written (as an existing qualified pilot however, I recommend the ASA "Test Prep" book, which should get you through it pretty painlessly), FAA PPL Checkride (comprising an oral, then a flight test - again, get the ASA oral book, and memorise it. I really mean memorise.) Also learn your way around FAA charts, and the US government weather forecasting system.
In my opinion, not having flown with you, your profile suggest you'll need around 10-15 hrs of instruction to meet the checkride standard. What PatoWalker has posted is correct, but also download the FAR AIM 2019, read all of it (that will take a while), and check in there any detailed interpretative material about requirements. There may be stuff not in part 61.
G