Large gap appeared between Flute 1 and 2 staves in Orchestral Score

Well, no. You have several multiple reheasal marks, A to D (3 times each) and E (6 times!). You can/should have only one per system, as reheasal marks attach to / apply to systems, not staves (asme as for example tempo markings).
Those (single reheasal marks) do get replicated into the parts (which you don't yet have, but could create via File > Parts > All parts, check the attached)

Also "dragging down" is not the way to go, really, much better is to use the Inspector and the offsets there, possibly along with disabling autoplace

"Trumpet 1" will never ever play directly from the main score (not in an arrangement with that many instruments for sure), this is for the conductor (and the conductor only).
Instead Trumpet 1 will play from his/her separate(d) part. And that will have the rehearsal mark right where it is to be expected (see the above attachment).

To be clear: what you did to cause the problem was your "workaround", but more specifically, the fact that you failed to disable automatic placement for one of those adjusted rehearsal marks. But also, the workaround you chose was not a good one - it was more work than necessary, and it's also "fragile" (meaning the adjusted position will turn out to be wrong if the score layout changes for any reason).

Rehearsal marks are not normally meant to be repeated on each section; that's just not how music is normally published. But in large scores like this, they are often repeated once above the strings. So that particular set of extras is good - just not the way you created them,.

Instead, simply add plain staff text to the desired staff directly, but assign the rehearsal mark style using the Inspector. Either way, you will also need to mark the extras invisible in the individual parts.

MuseScore 4 will provide a way to automatically show these marks above given sections, although it's not clear yet if that will actually be supported for anything but the specific case of strings in an orchestra.

BTW, I'm not sure what you mean about finding the duplicate rehearsal marks useful when entering notes, but perhaps it's because you don't know about the "FInd" command (Ctrl+F) that allows you to jump to particular locations quickly and easily. So you can jump directly to letter D by pressing "Ctrl+F D"). Or maybe you mean, while entering music for strings left to right, you want to see when you've reached letter D. A useful way to simplify writing in sections like this is to generate a specific part for each section specifically, using the "Single Part" button in File / Parts and adding the specific instruments you want. I think this was hinted at in the discussion, but I didn't see where it was spelled out directly.

Not separate systems, but parts, generated from (and linked) to the main (conductor) score. I guess you mean that though