What version of Finale created the old score?

That I do not know but it would have been a fairly recent one. The last major release would have been the oldest.

OK, I'll assume that you didn't do the export then.

Have whoever did, download and install the Dolet 7 plugin for Finale 2009–2014.5 from MM. It's two versions of MusicXML newer than was included in Finale 2014. Then have that person export the score again.

http://www.musicxml.com/dolet-plugin/dolet-plugin-for-finale/

If the export was done from an earlier version of 25, have him/her update to 25.4.1.

To have Finale not print "Score" at the top of every part, you have to replace the text field in the score with an insert (from the text menu) that calls the Text > Inserts > Score/Part Name option. Presumably this existed in the original score but was translated to plain text as part of the XML conversion.

If what you imported was the score, you can redefine the page defaults for the Parts in the Document Menu to place your Title, etc. properly and then regenerate the parts from Document > Manage Parts or else Redefine the format of individual parts in the Page Layout Menu.

Clarification: I exported and imported using the latest version,

I got "Score" changed to the part name.. 

However, the text (subtitle, part name, composer) does not appear in the same location on the part as on the score. The title is in the right place but everything else is shifted way down.

Updated the page layout and regenerated the parts but the text is still shifted way down.

… the text (subtitle, part name, composer) does not appear in the same location on the part as on the score. The title is in the right place but everything else is shifted way down …

The difference could be caused by having different scaling percentages in the score and the linked parts.

In the score you need to have all the staves on the page.

Hence it is necessary to scale the page down.

A text block’s vertical distance down from the Top Margin is decreased accordingly.

In a linked part the readability is essential.

Hence it is necessary to scale the page up.

A text block’s vertical distance down from the Top Margin is increased accordingly.

Solution:

Use two different text block positionings: - one in the score, and another in the linked parts.

To get different positionings in score and linked parts you must “unlink” the text block’s positioning.

This “unlinking” can be done via the text block’s context menu (you must be in the Text Tool).

When I place text notes within the score it does not stay in the same location on parts. Dynamic markings and expressions will transfer correctly.

… When I place text notes within the score it does not stay in the same location on parts. Dynamic markings and expressions will transfer correctly …

If I understand you correctly, you need the text blocks to “stay with the measure” (as text notes about that measure) - similar to expressions, right?

To make this work the text block must be measure/staff attached, rather than page attached.

1) If you attach the text block from Scroll View, it will automatically be measure/staff attached.

2) To inspect/edit a text block’s attachment, drag-select the text block’s handle.

Then go to

Text menu > Frame Attributes…

Or use the keyboard shortcut.

The general keyboard shortcut (which also works on expressions) is Shift-Return.

3) When you are in Page View, all new text blocks will by default be page assigned:

Text menu > Assign to Page

But in Page View you can choose that instead new text blocks should be measure/staff assigned:

Text menu > Assign to Measure