Signs of bad u-joints, vibration in the driveline, clunking noise in the driveline, severe play in the driveshaft. Yes your driveshaft will have some play in it. That is why you can turn the driveshaft a little right now. That is mainly because of backlash which allows for play between the pinion and ring gears in the diff.
Your leak you have would be the pinion seal. Marc talked about replacing this seal once. I am not clear on what it takes. Besides disconnecting the driveshaft and removing the yoke, and then removing the seal. I know you have to torque the yoke nut back down, don't know the proper torq specs and I am also unsure if there is shimming required when you replace the seal.
If you only have an oily residue on your diff I would not worry to much about that seal unless you have puddles of gear lube underneath the front of the diff.
U-joints I replaced my stock ones back around 75,000 miles. I now have aftermarket greaseable ones in it that have 75,000 and still in good shape.
Lifting a truck can cause premature u-joint failure.
Also your carrier bearing if your truck has one aka driveshaft support bearing will go bad as well. This will cause a vibration and squeek and shimmy when it goes bad. The only way to replace it is to remove the driveshaft and have the old bearing pressed off and the new one pressed on.