How can you tell what needs to be replaced when dryer starts squeaking?

Squeaking is usually the belt or a bearing. Thumping is most often the drum rollers. You will have to open the case and check. Sometimes you can remove the lower plate and find the culprit.

These dryers will do that when the lint builds up like concrete on the inside of the air ducts and the bearings get dry. Halfway cleaning it will not work. You need to totally tear it down and scrape out and wash all of the parts except the motor, which you vacuum out. You can go to YouTube to see videos on how to take it apart, but do a very good job or it will fail quickly. I would get a new belt and change it while you have it apart and get some white lithium grease and grease any and all bearings you find. You need to clean out a drier every two years, at least, according to the manual. You just unplug the wires from the sensors and remove ductwork that they are attached on and clean the entire thing with soap and water. Make sure you go all through the dryer and get all parts like the blower fan and housing, vacuum out motor well and clean exhaust. Mark all wires you unplug so you know where they go. This is an easier job than you would think. Make sure to clean around all of the sensors, too, because when they cannot sense the dryer will not work, plus the burning lint deposits will burn down your house. (Dryers are a leading cause of house fires.) See: Dryer vent cleaning prevents fires - YouTube and: Cleaning out a dryer with top lint cleanout - YouTube
Cleaning out a dryer: By a woman 2 of 2 - YouTube