Working away

You might get weird looks but I'd recommend packing a food scale in your luggage and using it at restaurants if you have to. Generally speaking though most restaurants are more than happy to tell you what's in your food so give it your best shot. You also don't have to eat out at restaurants every meal, I have coworkers that frequently use their per diem to shop at a grocery store for their meals. Could always visit the local grocery hot bar then use your food scale to measure portions exactly.

As for exercise, most hotels at the minimum (if they have an exercise facility) will have free weights and a tredmil. If they have dumbells then dumbell stopgap is a great exercise while away. If there's no tredmil or exercise facility there are gyms that have day passes, golds is $10 in my area.