When I first got my Jeep running, I put it in low range, and it started making grinding, scraping, and clunking noises and the lever wouldn't go all the way down. Maybe I wasn't doing it properly. How do I shift to low range properly? If there is something really wrong, will trying to put it in low range again break anything? It seems to shift into low range fine with the car off.
My jeep has the normal transfer case that does not have the non-locking 4 wheel drive.

Cue cruiser54 in 3...2...1...

You may need to adjust the linkage.

Pete will chime in with the proper procedure soon,, I'm too lazy to search for it at the moment, haha

Yeah, the linkage is likely out of adjustment. The proper way to engage 4 low is to pop the transmission into N (or push in the clutch) while just barely moving forward (or backwards, I suppose). Then give the transfer case lever a nice firm tug all the way to the rear from the 4 HI position. Rolling forward slowly is key.

I did not do it that way. If I try it again and it still makes those noises will it break anything?

How did you do it? If you left it in D, that's your problem.

I was not rolling, but I put it in neutral. At least I think I did...

Here's how the factory suggests you shift the transfer case and I've been doing this since these things were new and I worked at the dealership. Quoted from the owner's manual. The suggestions in CAPS are mine.

"To engage, shift the transfer case lever from 2H to 4H while the vehicle is moving at any legal speed". I LET OFF THE GAS, THROW THE LEVER, TAP THE GAS AND LET OFF.

4L position: " To engage, slow the vehicle to 2-3 MPH , shift the transmission to Neutral, then shift the transfer lever to the right and pull firmly rearward to 4L".

TO SHIFT OUT OF 4L, SHIFT THE TRANSMISSION INTO NEUTRAL WITH THE VEHICLE STOPPED, SHIFT THE TRANSFER CASE LEVER TO 2H, THEN THE TRANS TO D IF YOU HAVE AN AUTOMATIC, OR INTO FIRST GEAR WITH A MANUAL, AND CONTINUE ON.

Does the transfer case have a full load of fresh fluid? Ever checked?

I tried, but I couldn't get the bolt off.

That's one hell of a stone to leave unturned.........

Start spraying it with penetrating fluid a few days ahead of time. I've had to resort to the impact wrench on a few. Is it the big hex nut, or the style that takes a hex key? The head on the large nut shape is pretty thin and sockets barely engage on it. If you manage to round it off, a big pipe wrench and a 2-lb sledge is the next step. Yes, make sure you can get that fill plug out before you drain it.

When I roll forward and engage 4Lo, it works. When going downhill in gear 1-2 in 4Lo, I can hear a quiet whining sound that goes faster and a little louder when the vehicle gains speed. In gears 3 and 4, I usually don't hear it. Is this normal?
Also, spraying the transfer case bolt (hex nut) with penetrating oil a few days before did not help.

Pretty normal. I'd say if you're getting into 3rd or 4th, you may not need to be in 4-lo.