’Assalāmu ‘alaikum wa rahmatul-Lāhi wa barakātuh,
What are the general stress (I do not mean nabr) rules of Arabic words, if there are any? I guess that a “long” vowel automatically has the stress, but sometimes there are no or multiple “long” vowels in a word. Maybe the concept of stress does not exist in Arabic or it is allowed to stress multiple syllables in a word?
Jazākal-Lāhu khairā.
Salāmun ‘alaikum wa rahmatul-Lāhi wa barakātuh.
Answer
Wa alaikum assalaam wa rahmatullahi wa barakatuh. We are not experts in linguistics, so can only speak from the aspect of Qur’an recitation and tajweed. Outside of 
there is no stress required or demanding in reading the Qur’an. There is a natural sort of stress, and we are cautious to use the word "stress", when stopping on a word that two sukoons due to the incidental sukoon on the last letter when stopping. This stress is not part of tajweed though and is just a natural outcome of two letters with no vowels being pronounced one after another.
We would differ with the questioner in the thought that there is stress with mudood letters since they come out with ease and without extra effort, and there is no acoustical stress when pronouncing them.
There should not be stress on one syllable over another in the recitation of the Qur’an.
For more details though, we suggest you contact an Arabic language expert, since there are many things studied in the linguistic Arabic not part of the recitation of the Qur’an.
Wa iyyaakum. Wa assalaam alaikum wa rahmatullahi wa barakatuh.