So if I am mindful of let's say a sensation or I am just mindful of a specific body part
This statement is wrong understanding. Mindfulness does not mean to be aware, conscious or observant of a sense object. Instead, 'mindfulness' means 'to remember' to have right view towards a sense object. Please refer to MN 117.
should I label that "event", e.g.: thinking, thinking, touching, touching, seeing, seeing?
No; unless you are a complete beginner who must develop conviction in the truth of the teachings or unless you are dealing with a difficult to manage hindrance or distracting thought.
If you label every experience, your meditation will become very busy & convoluted.
Please refer to MN 19, where the Buddha-To-Be labelled things for the purpose of preliminary understanding but later made the mind quiet for the purpose of developing concentration.
I am asking because the buddha also said that one should use sati in tandem with comprehension
Correct. 'Clear-comprehension' (sampajanna) simply means 'active-situational-wisdom'. However, 'sampajanna' is not merely labelling things in situations where labelling is helpful. 'Sampajanna' also knows when to keep the mind quiet when the mind needs to be quiet, such as when developing samadhi (concentration).
As for 'sati' ('mindfulness'), its role is to remember or to bring/deliver 'sampajanna' (situational wisdom) to specific situations.
therefore one should constantly remind oneself of the three characteristics.
Very good. This statement is correct understanding. 'Mindfulness' means to 'constantly remind onself' and the 'three characteristics' is one type of wisdom that often needs to be applied in the development of concentration (samadhi) & insight (vipassana).
This said, there are many types of wisdom & understanding that sati-sampajanna must use.
So first the labeling and then a short contemplation of the 3 characteristics
Correct. This is preliminary understanding (Right View, 1st factor of eightfold path) that must be reflected upon & used so the mind can develop the path.
However, once the path & concentration is developed. the three characteristics will be directly seen & known (which is vipassana).
Therefore, the three-characteristics as 'sampajanna' is required to help you develop the path of concentration. Where as the three-characteristics as 'vipassana' is an automatic result/fruit of developing the path.
How are you guys doing mindfulness in buddhist terms?
As described. 'Mindfulness' means to 'remember' or 'constantly remind onself'.
In my practise of mindfulness, the primary thing I remember to do is keep the mind free from craving & attachment because sampajanna knows freedom from craving & attachment is the cessation of suffering (according to the Four Noble Truths).
If craving & attachment arise, then I remember (sati) to apply different wisdoms (sampajanna) to eradicate that arisen craving & attachment.