This app was mentioned in 9 comments, with an average of 1.56 upvotes
Just one? Or both of them? Cause if its just one, you can use button mapper to remap it so a short click lowers the volume, while a long click raises it, or something like that.
There are also quite a few apps (example - https://play.google.com/store/apps/details?id=com.mortisapps.trayvolume) that place volume buttons in your notification area.
It's a 'feature'. Android Lollipop (5.0.0 onwards) introduced a new(ish) volume management system, where silent mode only applies to any notifications or alarms, if you play music or watch a video it will default to whatever the volume was when you last used that app. In theory, this wouldn't be so bad except there is quite a delay when opening a video/playing music so that pressing the volume buttons in a panic to turn it down doesn't work for at least 5 seconds. I suggest installing a volume manager to place a widget that you can manually reduce volume with, because Google loves changing things for no good reason, often for the worse.
Edit: i personally use this one TrayVolume I'll go more into why it happens, there used to be just one volume slider, but the new system uses multiple, one for notifications (the default when no apps are open) & one for audio (music/video), so the notifications can show no volume before you open an app, but when you open a video it's actually reflecting the setting of the audio slider instead, and annoyingly you can only change this if you prefer to use the volume buttons WHILE AUDIO IS PLAYING, which is just a really top-notch, splendid idea.
Notifications being dim--no fix for this, it's how ambient display works. You can download apps like lightflow (typically used for the LED notification light, but has the ability to affect display behavior when notifications come in)
Multiple emails consolidated in notifications--if you drag down on the gmail (or email app) notification, it should expand each message, showing you more info and some of the email body text.
Notifications for unnecessary things--you can enable developer options, and then you can turn on granular notifications which allows you to change the notification behavior/amount of notification on an app-by-app basis. You can turn off notifications for the google play store if you enable this. You can alternatively do this without developer settings if you go into the app tray, long hold the play store icon and drag it up to the "app details" tab at the top of your screen. From there you can set it to not display any notification content.
Status bar clutter--if you adjust the notification settings for annoying apps, this will go away.
Quick settings hard to interpret--I don't agree; if an antenna is turned off, the icon has a bar through it. If an antenna is on but not connected, it is gray. If it's connected, it's white. If a setting is off, the icon is gray. If a setting is on, it's white. To be honest, I hate iconic representations of statuses, and wish it just had "on" or "off" in text...
The fingerprint icon on the lock screen--this is not obvious, but if you have smart lock turned on for your phone, where it will not require a pin or password or fingerprint to unlock the screen if you are in a certain location or connected to a specific Bluetooth device, that fingerprint icon is important. It turns into an unlocked padlock if a smart lock device or location is present, indicating that the pin/fingerprint requirement may be bypassed. But if you long press that icon on the screen, it turns back into the fingerprint icon and a text displays over it saying, "device will stay locked until you manually unlock". It will force the use of fingerprint or pin to unlock the phone the next time you swipe up on the screen. Convenient if you're in a public place and use secure lock, but don't want to turn off secure lock globally and just want it to not function for that specific period. It's completely unobvious that this icon has significance, so I totally understand the confusion of why it's there in the first place--one thing android is horrible at is knowing whether something has a purpose or is just aesthetic, and what some very useful but totally unadvertised functions do.
App drawer search--another unobvious and unadvertised thing which addresses your desire specifically--if you find that little up arrow indicator on your home screen that indicates dragging up to access the app drawer--but instead of dragging up on it, you long hold on the up arrow, it will open the app drawer into the search field and launch the keyboard, doing exactly as you wanted.
No overlay volume slider--I can't verify because I'm using a different rom, but I think this is not in stock. However, you can use a multitude of apps from the play store like the one below--the integration may not look elegant, but accomplishes the functionality you're looking for, and you can toggle volume from the tray: https://play.google.com/store/apps/details?id=com.mortisapps.trayvolume
Hope some of these things help. If it makes you feel better I have the exact same feelings of frustration and confusion when I'm forced to use an iOS device!
This one sits in the notifications https://play.google.com/store/apps/details?id=com.mortisapps.trayvolume I used it on my kindle fire which had no volume buttons.