Help Lollipop woes

As you know I'm not on a Sony, so this is fwiw -

On #4, try to long press the notification - you may get an option to block or prioritize.

I like the behavior in #1 and will be sorry to see it go.

Lollipop ART ought to result in apps opening at ludicrous speed. The only thing that I can think is going on, and this may also help the music problem, is that they have the out of memory minfree values completely hosed and the launch delay is being caused by some chicken dance with swapping apps to cached storage to get sufficient free ram for the app launch.

A quick and dirty test of that theory might be to try developer options, advanced, and limit background tasks to 3 or 4. If that shows promise try any of the zillion OOM minfree setting apps and adjust from there. (Developer options doesn't require root, changing OOM minfree values does.)

RAM Truth or System Panel, both from the Play Store, may shed some light on the available vs free ram situation and aid in the adjustments.

You are not alone.
The UI is actually starting to grow on me, at first I wasn't sure about it as, like you say, I thought it looked very childish, but I think it's quite easy finding things with the new notifications etc. I think they have gone for something and not really thought about it in any way, too big an overhaul, hopefully in the next version they will roll back to something more like Kit-Kat. And as you say the smart unlock is a hell of an improvement with face detect.
My biggest gripe with Lollipop is the lag you mention, I really don't think I have ever been lucky enough to have an app open in 10-15 seconds. Also even when going back to home pressing the home button you can be sat there for several seconds waiting for the icons etc to actually arrive on screen. Do you find that? I suppose I'll try a wipe and reflash, just hate the backing up etc and then gambling on if all my settings will be restored. I know there is a major memory leak in the Lollipop framework but I heard that Sony fixed it anyway in their ROMs as there is a patch out there somewhere that fixes and it says sorted in there. I'm not convinced.
I am still having major battery drain compared to Kit-Kat too, I HAVE to charge it every night now, I was able to let it run through the night not on charge and perhaps charge it throughout the day instead. Now even if I charge it in the day I have to charge at night to be safe anyway.
I've not noticed any issues with Camera. Could it be ROM related or are you just running stock?
My apps often close themselves, even if it is just one thing running, eg, Deezer, got earphones in and suddenly will stop.
I think you could be right with the sound. I am using Viper mod but I think it's still not up to as good as was.

In all I think Lollipop was a huge disaster for Google to be honest. They must know how much of a flop this has been and surely working on a major update to fix all this and actually make it smother and faster as promised...will have to wait and see...

This is crazy.

We both have 2 GB RAM, both have about the same Available and Free, you have a Snapdragon 800, I have the 801 (specifically the MSM8974AB). Not enough to explain the huge difference -

http://www.anandtech.com/show/7846/...-snapdragon-800-and-801-clearing-up-confusion

Mine screams on stock, unrooted Lollipop 5.0.2 (vendor modified).

I know it doesn't help but this has to be on Sony's side so hopefully they'll update it quickly.