Well, as usual, while I was preparing this post, you snuck one in on me (chortle)...
So, first things first.
Example 1. Yes. the RC constant (rise time) to full charge is so short (100msec) that it looks like a straight line when your time base (5) is that long,
Try the transient analysis again with the "End Display" time set to "100m" (100 milliseconds) and you'll see the classic rise curve.
Example 2. Fine.
Example 3. Now your rise time is too short for the time base.
Try the transient analysis again with the "End Display" time set to "10" (10 seconds)and you'll see the entire classic rise curve towards the 10 VDC rail.
Example 4. It looks your capacitor is set to "1k" (or, 1,000 μF). That being the case, your time RC constant is 1MΩ X 0.001F which gives an RC time constant of 1,000 seconds, or 5,000 seconds for 98% charge (or 1 hour and 13 minutes). As a result, your trace was only 5 nanovolts (5 millionths of a volt) above zero after 5 seconds. And too, it looks like a straight line because for that brief a period ( 1/1000ths of the RC constant) it should.
Good job, Graham.
Some of these comments should address some some of the voltage values you saw. If not all of them, give them to me again. On that note, the capacitor will eventually always charge up to the battery (or voltage source) level (unless stopped short by some other component or circuit). In these simple circuits, it will always get to VDC max (although mathematically it never does. It is an asymptotic function [A curve and a line that get closer and closer to each other but never intersect]).
Don't you just love it??
CBB