What is your opinion about this - if prasādam is pure then there´s no fault if you don´t wash your mouth after eating it?
ācaman is a Vedic and Vaiṣṇava duty. Such duties don't cause offence to prasād. Though you can swallow the water instead of spitting it out. When you brush your teeth you also remove prasād from your mouth, that cannot be avoided completely - not to speak of digesting it and turning it into stool. You destroy it by chewing it. Though no sacred object is to be put on the floor, we take prasād from a plate on the floor too. Respect and bhakti are a matter of attitude only. Kṛṣṇa knows your attitude within your heart.
I remember it is somewhere in śāstra that external habits and actions of the Guru should not be copied?
advaitaṁ ca parityajet (Haribhakti Vilāsa 1.89) - it is forbidden to copy [dvaita] the Guru, be a second Guru [dvaita]
Actually it looks that it is one of main reasons of vaiṣṇava-nindā - this tendency to copy someone. Why? Because copying means that you associate devotion with certain external characteristics - which it is not. Just as Puṇḍarīka Vidyānidhi and Gadādhar Pandit - Gadādhar accepted Puṇḍarīk as Guru but never imitated him. When you have a certain pattern, "ideal" of externalities....
Yes, all that too, but to copy the Guru also means you want to take his place.
A "hedonistic" gṛhastha would be the Guru of a vairāgi and vice versa. I think that's why it is forbidden. A vairāgi cannot copy the behavior of a gṛhastha. Every jīva is unique. You cannot become "as someone".
Well, yes, that also. There is anusaraṇa and anukaraṇa - following and imitating. We should follow the Guru, not imitate him.
We can immediately understand who is the Guru of a devotee who gives a lecture. Most of them are copying the manner of speaking of their Guru.
Yes. Such imitation can be a type of bhakti, but it is forbidden still. It is artificial.
One of the biggest reasons of aparādha is when people think "This is such-and-such bābā - he is so sweet, an uttama bhakta, his manner of behavior is the highest." And when they meet some externally harsh guy "uff, this person cannot be a pure devotee, his behavior is not sweet". Our Baba once beat his [male] disciples for starting Tulsi-kīrtan while he was still speaking.
Hari bhakti vilāsa (1.99) quotes the Viṣṇu-smrti - na guror apriyaṁ kuryāt tāḍitaḥ pīḍito 'pi vā - The disciple should not displease the Guru, even if he beats or torments him. This obviously applies to very surrendered disciples. Weak and selfish disciples will otherwise hold a grudge agains the Guru, which will ultimately destroy their bhakti. Sweetness is a saintly quality but you are right, harshness can be very pure too. Our Baba was as soft as a flower and also harder than Rudra - bajra sama rudra rosh o kusum komal āśutosh. Rudra can be hard as a thunderbolt or He can be Ashutosh, easily pleased.