New to me Dodge Ram 1500 5.2 liter automatic
 

Problem #1 After driving the above vehicle for twenty minutes or so, when I apply the brakes the truck shudders a bit. The more I drive and apply the brakes the shudder becomes more pronounced.

Problem #2 On a recent trip of about 125 miles, I noticed at about the halfway point of the trip that when reaching the top of a hill that the transmission was not shifting out of first gear back up to fourth when going down hill. Also the tachometer was staying in the 3000 plus RPM range at 50 MPH. After stopping the truck and shifting into neutral, the truck shifted back up through the gears in drive (no overdrive) to fourth as normal. Later, still going down hill it seemed to want to remain in first or second gear for no reason for periods of time before going to third and then fourth. It completed the last twenty miles or so without any issues. Being unfamiliar with the truck, I did notice that it seemed to want to drop down in gears more readily than I am used to and did not return to fourth until well after it seemed like it should.

At this point I have not done anything with the truck. I would much appreciate any thoughts on these two issues. Thank you