How many Game hens can I cook at one time and for how long

I would go with 450F oven and start checking the birds after about 25 minutes, having rotated / swapped pan positions after about 15 minutes. As pointed out above, taking the temperature of the meat is the only way to know if they are properly cooked. Let them go a bit longer if they need further cooking.

In the interest in being complete, I suppose it should be pointed out that the game hens should not be touching each other during the roasting.

They won't roast properly where the flesh of two birds touch each other. This is why rotisserie chickens are often roasted on rotating spits, to minimize contact.

You may want to truss the birds so they are a bit more compact. This is not a preparation that benefits from crowding the pan.

Don't cook by time, cook by temperature. They should read 165 degrees F on a meat thermometer.

This is even more important because you are roasting a large number of birds and the typical household oven doesn't maintain an even temperature throughout the entire oven. There are hot spots and cold spots in the average consumer oven.

I would try to roast eight birds on two sheet pans. You will want to rotate and swap the pans a few times to help cook more evenly.

If your oven has a convection fan, use it to help promote air circulation.

They won't all reach the target 165 degrees at the same time. If you have a remote meat thermometer, you can stick it in one bird, but you should start doing spot checks of the birds starting around 150 degrees because some may cook faster than the bird with the probe. Use an instant read thermometer and measure all sixteen birds starting with the birds that visibly look more done than the others.

One by one as they arrive at 165 degrees, set those finished birds aside. I suggest using one of the disposable aluminum serving pans, the kind people use at picnics, tailgates, etc. Cover with aluminum foil to keep the birds warm.

Best of luck.