[*]The stock email, calendar and tasks apps are not good (for my needs).
I don't know what your needs are, but take a look at Cozi. We use it as a calendar and task app to coordinate a family spread all over town.
[*]The Gallery app is better than the Google+ Photos app. Actually that is still a bit confusing. Why have two apps for the same thing by default on the device? The Google+ app even displays some of the pictures that I have on the Gallery app, but I still haven't figured it out..
Most of the picture apps on Android use Media Scanner, which basically builds a list of media files (or several lists - videos, audio files, picture files). Gallery doesn't have its own directory.
[*]Browsing the file system is still a bit confusing for me. I have read articles that describe its structure, but I thought sdcard would be my externa MiniSD card, but it wasn't. Sdcard2 is the external SD card. Is it always like that?
Since Jelly Bean, I think. Someone came up with "internal SD card" - which is an area of EROM simulating an SD card, so phones that don't have SD card slots could use apps that save data to the SD card.
And now, with 4.4.2, the external SD card is no longer just a FAT32 card with no security. As I understand it (it's new, so I'm still learning), most directories on the external SD card have write permissions only for root and owner, so other apps (and external computers) can't just write data anywhere on the card.
[*]Does anyone know where I should save ringtones? Which directory? Can it also be on the SD card or better not?
They're picked up by the media scan, so they'll work either way. I keep mine in /mp3/ringtones (and /mp3/alarms and /mp3/notifications) on the SD card, so if the phone goes bad (I wasn't watching what I was doing the other day and flashed a keyboard where a ROM should go, so I lost all data on the "internal SD card", as well as the rest of storage), I don't lose them.) It's a personal choice, really. You could also use /ringtones, /alarms and /notifications - Android isn't fussy.
[*]Chrome: It's very good, but lacks read mode (as Safari does). I know there are other browsers out there that have it, but I would prefer to use Chrome
One problem with Chrome - it doesn't support Flash, if that matters to you. Dolphin and Next do.
[*]Notifications: I think the way iOS handles notifications for apps is better. I have a central place where I can go and see which apps are enabled for notifications. On Android I have to go to each app and see its own setting. Is there any way to change that somehow? It doesn't bother me, but I think it's not the optimum way of doing things (or I am just used to iOS so much)
Since Google doesn't impose that restraint on app developers, no. (Remember, to write an iOS app, you have to know C. To "write" an Android app, you can use drag&drop templates, and not know programming from horses.)
[*]Battery life: It's difficult to say something about, since I am playing with the device all the time. Charging the device is slow, it could be much better. Battery life seems to be very good also.
Remember - condition the battery - 3 full cycles of full charge, then discharge until the phone tells you to recharge. And the best battery lifespan is recharging at the 40%-60% area. Nothing to do with Android or iOS, just how LiIon batteries work. If you root, install Xposed and Greenify, you'll find a pretty nice increase in battery life.
[*]MX Player Pro (very good video player - what is the default app actually?)
Manufacturer-dependent, I think. In Samsung it's Video.
Try Total Commander too. Each one has its strong and weak points. I keep them both in a "file manager" folder on the desktop.
[*]AirDroid (amazing app to control your device remotely)
Agree. There's also ADB wireless if you want to save the microUSB port some wear. (Worst standardization choice I've ever seen - a flimsy port that's used a few times a day by many people.)
[*]1Password reader (I hope they bring a full featured 1Password client soon)
KeePass (Mac, Windows, Linux, Android ...) I keep the data file on the cloud, so all my devices are always using the same passwords. You have to use the Home key in Android a bit if you don't have a multi-window function.