ADP/AGI is a new attribute in DkS2 that's worth getting familiar with. It affects how fast you can use things like estus, how many iframes you have during rolls and backstep, etc. When ADP/AGI are low, some things seem more sluggish or you get hit more often than you think you should be hit when dodging etc.
DkS2 also queues and executes button inputs differently than DS1. In DS1, you could input a button press during an action and that queued button press would follow. DS2 does not do this so it can seem less fluid if you're used to that older queuing. Concrete example: go back to DS1 and mash the square button to queue a heal during an attack action. You will heal after the attack. Do the same thing in DS2. Nothing will happen after the attack. It's just a difference that takes some getting used to.
Another huge difference in DkS2 is that running (holding down circle button) consumes a massive percentage of the stam bar compared to DS1. This means that with DS2, you will be constantly releasing/pressing the run button if you are just running for a while between areas etc. Concrete example: go back to DS1 and just run with a quality build for as long as you can before your stam bar depletes. It will take a really long time compared to DS2 with roughly the same quality build breakout. You'll notice this the most with DS2 when you start out because your stamina is lower and it feels like you're stam bar depletes so quickly when running compared to DS1. But this again, you get used to.
I also agree with you that all of the "timed" delays in DS2 are absurdly long for veterans that just want to get on with it. You can go eat a sandwich and come back to riposte a parry you made. Opening chests takes much longer than it should IMO as well.
But there are reasons behind these decisions. A massive riposte window let's you ring swap 10 times, switch to a dozen different weapons, and then embarrass your opponent with a pivot backstep before riposting. Or not. And it's here that veterans could properly do ring and weapon swaps in less than half the time the window gives you so all of these delays are way too long IMO.
On the estus shards, you get 12 max and a +5 healing bonus using up to 5 sublime dusts. There are no firekeeper souls in DkS2.
On the halberds you mention, BKH in DS1 was very OP for PvE. For DkS2, you may want to try Mastodon Halberd which is a STR halberd that drops from Mastodons. It can deal some damage, has an "A" STR scaling at +10 etc. It can be farmed earliest from a Mastodon behind a fragrant branch in Heide's Tower after 2nd bonfire. If you don't get it before despawn you could join Covenant of Champions and spawns will happen again and then you can abandon the covenant with tupac shalquior the cat afterwards. Abandoning a covenant costs nothing and affects no covenant ranks or rewards. If you're newer to DkS2 covenants you may think abandoning a covenant makes you lose something but it doesn't, you can rejoin and pick up where you left off.
On the floaty knight dude, Pursuer spawns quite a few times in Bastille area and is a great chance to get early twinkling titanite drops.