Question from beginner: do I really have to count out loud?

Yes. Counting will help you with the following things:

1. Understand the written rhythms correctly, and play accordingly.
2. It generates feedback for yourself whether your timing is correct.
3. It tells you whether you play fluently and where you are rushing or dragging or, waiting to long all together.

Counting in your head does not work for beginners. You need to hear it be part of the music to make sense of it. As a teacher I am confronted by this all then time.

Not counting is easier, but it’s something you have to get familiar with. It helps a lot with feeling the music as it should be felt, and understanding what’s really on the page. Rhythm is something you think you do correctly until someone shows you you’re doing it wrong.

It is a subject where you cannot really trust yourself you’ll do it right, because your ears will accept pretty much anything (unlike wrong notes).

TL;DR You are your own teacher so you have to generate feedback for yourself.

You dont need to count aloud, but you should move your lips as if counting aloud. It does help to syllabalize.

at some point you will want some or other (non lips) body movement to convey the counted-beats of the bar (and many movements seem to suffice). Think of them as the “coordination control”, onto which you then impress the particular notes of the score. Only once you can walk bipedal-ly can you then do 15 different dance steps, as it were.

some folk call this a “basic rhythm” that orchestrates the movements of the body - upon which one superimposes the rhythms of the notes in the score

You’ll find two schools of “basic rhythm” - which Ill call angular and circular. With angular, you are essentially pulsing in and out toward/back from the piano lid. With circular you are making wrist circles/ovals. Its fun to watch YOUNG-phase prodigies move, and figure which they do (its almost always circular). Their circles fundamentally match the counting of the bar(s).

Honestly if its a simple rhythm there may not be much benefit to counting out loud. But when you start getting into more complex rhythm, dotted notes, 32nd notes, etc. then counting out loud while playing can be incredibly helpful to make sure you are playing correctly.

I do it on reflex when I don't know how to play a part. Although, not that loudly more like a whisper or biting down every beat. (Not noticeable so your teacher won't get mad, but may harm your teeth.)

Not at all. I studied music for 6 years and my teachers never really told us to do this.