Are there ways to have Mac OS recognize my password "better"? Basically I am "at odds" with Mac OS on how to properly type my password.

Meaning: when I used Linux (ubuntu with unity to be precise), I really didn't care about the "state" of my Linux box. If the screen saver/lock was up, I just started typing my password and hit enter. And ... I was logged in. Because the Linux screen lock was smart enough to understand that the string I typed + Enter is my password.

With Mac OS, on the other hand, I have to be much more "careful". I often find myself first type a letter, and press enter, and then when the input text field starts reflecting me typing ... I slowly type my password, and carefully press Enter. Because: if I don't do that, Mac OS will try to use maybe 5 out of 8 chars I typed. Or something else. So far too often, it takes me two, three turns before I successfully unlocked my screen. 

Long story short: is that me not fitting Mac OS (so I have to change my attitude of just typing pretty fast) - or are there ways to adapt Mac OS to my style of entering the unlock password?

(And yes, when I have the lid open, I use the fingerprint reader, works fine - but within the office, the lid is down.)
If you press the modifier keys (Command, Option, Control, Shift), it will wake the computer but not type anything, so you can press them as many times as you like without messing up your password.

I usually just drum on the modifier keys until I see the password cursor, after having exactly the problem you describe.