What exactly do you mean by "large", in each case?
Re: 1 - I'm not sure I quite understand what you mean. Is this in the campaign? Hmm, I think you mean combat, right?
If it's in combat, are you *sure* it's not your custom AI?
I mean, if we rule out AI and graphics, it doesn't leave much, and what's left doesn't care about whether stuff is visible or not.
If by "LOS display" you mean the fog of war rendering, hmm. That shouldn't matter since that's being done before you see the enemy ships also. It also doesn't happen unless the command UI is up.
Really, stuff triggered by seeing ships sounds makes me suspect the AI.
Re: 2 - Just tried buying every ship in the Hegemony station, and the Diktat one for good measure. With the fleet screen open, the FPS stayed at 60, with about 70% idle (90% idle being normal in the campaign, w/o the fleet screen being open. If you do find a way to replicate this in vanilla, please let me know.
(Might it be something related to custom weapon graphics? The ships in the stations generally don't have anything mounted. Just tried a huge fleet - 50+ fully fitted Odysseys, and lots of other ships - and that seems more or less fine, too. Only hiccuping a bit when picking ships up and putting them back down, and that's an unreasonably huge fleet.)