In one Sutta the Buddha said that one should constantly be mindful of the fact of anicca.

Sure. But you need to understand what the terms really mean.

Mindfulness (sati) means to remember.

Anicca is a wisdom (panna).

Sampajanna means 'situational wisdom', which is applying wisdom to a situation.

Mindfulness must remember to apply wisdom.

Therefore, mindfulness & wisdom always operate together.

There cannot be mindfulness without wisdom.

This is why the term 'sati-sampajanna' is often used, as a compound.

This video might help:https://www.youtube.com/watch?v=rpCy9Tb73gw&t=7s

This book might help: http://www.dhammatalks.net/Books/Bhikkhu_Buddhadasa_Natural_Cure_for_Spiritual_Disease2.htm

In the Satipatthana Sutta he said that when one is dressing, eating, speaking etc. one should be aware that he is doing exactly that.

Not really.

In the 1st part, about "I am walking, "I am standing", etc, the word is "pajānāti", which means to know. Here, knowing with wisdom is not emphasised. This is more about knowing with concentration.

In the 2nd part, about "going forward, looking ahead", etc, the word is "sampajānakārī". This not only means awareness but having wisdom with awareness.

As the video states, 'sampajanna' is of the wisdom faculty & not of the concentration faculty. Awareness without ready wisdom is not sampajanna.

Now my two questions (and yes I know that Sati is more than just present moment awareness in that it can also mean remembering something or calling somethibg helpful to mind)

Sati is never present moment awareness. Sati is only remembering or calling something to mind.

It is only those with wrong understanding who teach sati is present moment awareness.

Present moment awareness may be a result or outcome of using mindfulness but mindfulness itself is not present moment awareness.

Present moment awareness is simply a clear consciousness (vinnana), called 'anupassi' ('seeing') in the Satipatthana Sutta.

The aspect of knowing what one is doing is connected with mental noting, right?

Not really but sort of. Noting is a very subtle thing. Noting does not have to be strong thinking, as the Burmese Mahasi teach. The mind can note very silently, such as knowing it is typing on this website.

Because the Buddha never (correct me if Im wrong) mentioned to note something as seeing, seeing, touching, touching.. etc.

Of course he did, in the Satipatthana Sutta, that you mentioned, where it states: "I am walking", etc. However, this is only beginner's practise.

If I am not mistaken the Buddha said one should constantly dwell/remind oneself of the fact of anicca but at the same time one should know what one is doing.

There are many wisdoms apart from anicca. All sati-sampajanna includes some type of wisdom.

The Buddha did not actually teach to constantly remind oneself of anicca because this would mean the mind is always thinking. Instead, one only reminds oneself of anicca when necessary.

To goal of meditation is to stop thinking so the mind has concentration so it can calm and then see anicca directly (rather than reminding oneself about it).

This is confusing.

What is confusing is your views about it. Yes, you are making it confusing for yourself.

When does one know when to use "what one is doing-mindfulness" and when to dwell on "impermanence-mindfulness"?

When required.

Is continous present moment awareness actually endorsed by the Buddha? Kind of confusing because first of one cannot be mindful all the time and secondly, how is one able to be present aware if one uses sati in the "remembering" sense when for example a hindrance is present?

Your questions are like: "How & when & why do I do this turn when surfing and surf inside the wave when surfing?" before you have even learned to paddle a surfboard.

I think that the word "constant" or "continous" is just a word that puts strong emphasize on a specific activity, but I might be wrong.

I think you are thinking too much. When the mind has developed some calmness, it will begin to understand the teachings and what to do. Developing some calmness does not require the questions & answers.