The tranny lines go inside the radiator, there IS a serperate oil cooler for the tranny, but lines do go through the radiator.
It is so that your transmission gets to op temperature faster...go figure
I had the same problem as you, I got water all int he lines, they just flush it, it's not bad.
The only way to get water in your block would be if you have a bad head gasket or cracked head, but even then, your motor probably would not run right. I can almost assure you, you have NO water in your oil/motor.
As far as the tranny, buy one off ebay for 800, give them 200 to install it, it's a lot cheaper than a rebuilt for $2k!!!
08 Cummins Mega Cab, 7" on 37
02 Explorer Sport
08 Brute 750 on 29.5