If the Dreadnought misses his first attack is he stopped from further movement? Also, if the PC makes the strength save does that stop the dreadnought from further movement?
Nothing in the Shield Charge ability's description says that its movement is stopped by its attack during the Shield Charge. From its statblock:
Fireshield. Melee Weapon Attack: +13 to hit, reach 5 ft., one target. Hit: 22 (4d6+8) bludgeoning damage plus 7 (2d6) fire damage plus 7 (2d6) piercing damage.
Shield Charge. The giant moves up to 30 feet in a straight line and can move through the space of any creature smaller than Huge. The first time it enters a creature’s space during this move, it makes a fireshield attack against that creature. If the attack hits, the target must also succeed on a DC 21 Strength saving throw or be pushed ahead of the giant for the rest of this move. If a creature fails the save by 5 or more, it is also knocked prone and takes 18 (3d6+8) bludgeoning damage, or 29 (6d6+8) bludgeoning damage if it was already prone.
Judging from that, the shield charge lets the fire giant dreadnought move up to 30 feet in a straight line, including through the space of any creature that is smaller than Huge. The attack is essentially incidental to the move; if the target succeeds its Strength save, it is unaffected.
You could flavor this as if the character that makes the save is actually holding the fire giant dreadnought back just long enough to move himself/herself out of the way, or however else you want to describe it.
The dreadnought could, of course, choose to stop before the end of the 30 feet, since the Shield Charge doesn't specify that it must move the full 30 feet.
First, it does what it says it does:
Shield Charge. The giant moves up to 30 feet in a straight line and can move through the space of any creature smaller than Huge.
This is the part that says how the movement works - the rest is about the Fireshield attack and its effects on the target: it doesn't change this part about the giant's movement. It can move 30 feet in a straight line so long as it doesn't enter a Huge or larger creature. In normal movement, you can move through friendly creature's spaces but this specific action says you can only "move through the space of any creature smaller than Huge" i.e. friendly creatures can't get out of your way like they normally can. It doesn't change the fact that the giant still cant voluntarily end its move in another creature's space.
Second, remember that under the action economy, this is an action for the Dreadnought so they still have their movement, possible bonus action and reaction available.
Before and/or after this action (where it has moved anywhere from 1 to 30 feet or 5 to 30 feet if playing on a grid) it can still take its normal movement which can be in any number of directions.