is it okay to refer to "exhibit 1" and mention that it will be provided in person?
No. Attach them all in the pleadings/motions/briefs/etc. you file in court. You might want to elaborate why you think that would be impractical.
If by "provided in person" you mean "at the hearing", it will not work because other parties are entitled to get and review a copy. The judge might not even allow that, and ultimately he "runs the show" also at the hearings. Or if you mean "in person with the clerk", the clerk will reject it because exhibits are not to be filed separate from briefs, motions, etc.
Also, the approach you have in mind gives the adversary the opportunity to falsely and vexatiously allege that you never filed those exhibits.
if an exhibit takes up multiple screenshots (i.e. the libelous content), will each screenshot end up its own exhibit?
It depends on the [unspecified] particulars of your matter. For instance, if multiple screenshots are intertwined or pertain to one same event, it makes more sense to include them in one exhibit.
what if some of the exhibits are missing but are obtainable through another institution?
It is premature to call "exhibit" something that has not yet been exhibited in any of the filings. Once the other institution produces the records or evidence at issue, then they can be filed in the form of exhibits attached to the party's motion or response.
How would I write that the exhibit/evidence exists but that I don't have a copy?
This might not be necessary or even useful. Keep in mind that a plaintiff can subsequently file a motion amend complaint, wherein it will be possible to attach to it the evidence that was unavailable at the time the initial pleadings were filed.
If I can't get a copy before uploading the complaint (i.e. if the institution doesn't cooperate with my request), do I mention that this evidence is held by "institution x" so it could be subpoenaed?
Not necessarily. Subpoena (with judge's/clerk's signature) the institution, and in the meantime focus on evidence/facts you currently have/know. If the institution remains uncooperative despite being subpoenaed, you will subsequently file a motion to show cause.