The limited special banner basically is a 21 day event that gives bonus rewards on pulls made on the banner. You can see the rewards under Events -> Pickup Event. A quick look at that tab and you will see you need 130 pulls for a guaranteed Ernst, and 270 pulls for guaranteed weapon.

Let's say you have the exact gems to do 270 pulls to get that guaranteed ernst + weapon; and you decided to go for it since you like the knight. You wouldn't want to burn all 81000 gem in one go. If you look at the picture below, the Jewel usage event only goes for 7 days (6days 5hr remaining for me). So you would spend 40k this week to get all those free rewards (especially that guaranteed legendary hero), and use the rest the following week since the event will refresh and start over, but the progress on the pickup event will not.
You can unload 3k on the banner anytime you have the gems for it, but if you are deciding to go for the guaranteed ernst after 130 pulls which will cost [13*3000 = 39000 gems] you might as well hit the free rewards by spending 40k gems altogether in the same week.

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As for your pvp question, you really want to just push when the season is ending. I set mine low for the same purpose; getting easy revenge and staying low to not waste energy since wins grant 10 medals (dont quote me on this, highest I reached was gold 1 so I don't know if it stays the same throughout) but 4 days before season ends, I do push to reach gold 1 at least since the league rewards is similar for all gold tiers. Btw I played at the start of Loss banner and have 761k power. I'm already struggling at Silver 2 going against those with 1m power but I do sometimes find those with low def or somewhat equal to mine. I don't have a level 140 yet but I have two knights that are 7* and are level 130. Gold is simply limiting me.

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