Basic, basic trailer questions

Hello everyone. I'm building a Cubby, and have pretty much finished the exterior. I've never really used any sort of trailer, so I have a couple REAL novice questions. First, when the trailer is hitched, and I lift up on the tongue, should there be any freeplay. I've tightened that adjusting nut under the hitch enough so I can just barely close the handle on top of the hitch. There's still some "slop" however. Is this normal?
Second, I need some general tips on greasing. The assembly instructions call for filling the dust cap about 1/4 way with automotive grease. I did that. I took my trailer for a brief "spin" yesterday. After about 10 miles at 45mph, I felt the dust caps, and they were slightly warm. Is that OK?
Thanks for any info anyone cares to share. This group has been a great source of information.
Chuck
Second, I need some general tips on greasing. The assembly instructions call for filling the dust cap about 1/4 way with automotive grease. I did that. I took my trailer for a brief "spin" yesterday. After about 10 miles at 45mph, I felt the dust caps, and they were slightly warm. Is that OK?
Thanks for any info anyone cares to share. This group has been a great source of information.
Chuck