Export parts: phrase marks etc get all messed up in main, original, score

In order to really understand, we'd need to see the score *before* the problem happens, and then have precise step by step instructions to reproduce the problem. As it is, my best guess is that you made the mistake of attaching symbols to one place in the score then manually dragging them to *appear* as if they were attached to another. For example, there is no crescendo in bar 7 - it's in bar 6 but was apparently dragged put of position to appear somewhere else. That manual position might have appeared to look like it lined up with measure 5 at one point, but changes to your score later - probably having nothing to do with generating the parts - altered the layout of your score such that this manual adjustment no longer produces the result you intended. Simply attaching to measure 5 in the first place would avoid problems like that.

However, it's also possible you've been hit by an obscure/rare but annoying bug where sometimes the some system is right on the edge of being able to fit another measure or not, so the measure moves suddenly from one system to the next of its own accord. If this happens right as you save the file, then on the next load it might appear in the wrong place. Workaround is to notice that this measure migration is happening and to add line breaks to prevent it.

As Marc already pointed out, it seems you have dragged the hairpins far from their anchor points rather than attaching them at the correct position.
This is demonstrated even more clearly if you switch the view to continuous mode. Then you see that for example the crescendo now visible just after the last measure actually belongs to m47. Because its horizontal offset is now this big (119sp!) its off-page. This causes some of the rendering artifacts you're seeing.
Hairpins are now at the same position as the next page and MuseScore has trouble figuring out how to render this onto your score; the end result is that you might sometimes see them, sometimes not or only partially, depending on zoom level and the rendering of all other elements in view.

These rendering artifacts can also lead to unexpected layout changes. For me for example, with my screen/window size, after opening your attached score, I can trigger a layout change simply by double clicking the cresc that visually appears in m7 (but actually belongs to m6), then clicking the front anchor point (now you see the dotted line showing you it belongs to m6), clicking the final anchor point again and then click in the empty space between system 1 & 2, just above the starting note of m6.
At that moment, the hairpins that first appeared under the 'arrangement' text on the top of the page, now appear at the start of system2. I can make them show/hide by zooming in/out.

For this specific score, I'd probably go with; remove all the hairpins and start over. I've reset them all to their default position, but then you have quite a lot places with overlapping hairpins that it's likely just as much effort to start over.

This time however, to apply a hairpin, first select the range on which it should apply (click first note, Shift+click 2nd note). Then double click the correct hairpin in the palette. It will now automatically span the correct range and have correct anchor points.
Afterwards, you can still double click it, select an anchor point and then drag (or use arrow keys/inspector) for minor visual adjustments.
If you have to drag a hairpin more than a beat; it means you're likely going to end up with something wrong again.