How did you end up linking Salaat to Prayer - the prayer which is normally performed in ritualized/repeatable form, as seen in Namaaz, Christian Liturgical prayers, Jewish Amidah, Hindu Bhakti Yog, etc?
The closest the word ‘Prayer’ – as in an earnest request or wish - could come to is Du’a in the Qur’an, referring to the call of the caller unto God.
Salaat = To follow closely, like a runner-up (Musalli) follows the winning horse (Saabiq) = To follow Divine Commands. (QxP)
Aqimussallat = Establish the System that facilitates the following of Divine Commands. (QxP)
You again seem to be cherry picking the meanings of Quranic words to retrofit into Salaat so it could point to ritualized or some form of contact prayers. You have separated ‘establish’ from Salaat, and are stressing on the source qāf wāw mīm while ignoring the compound meanings of the word and variants “yuqeemunas salaat”, “aqaamus salaat”.
Here are some references on “establishing salaat” from Lughat-ul-Quran by Allama Parwez, your own oft quoted dictionary source:
2:3 And ESTABLISH and follow Allah's laws
Allatheena yu/minoona bialghaybi WAYUQEEMOONA ALSSALATA wamimma razaqnahum yunfiqoona
22:41 These are the people who when get established in the earth work to ESTABLISH SALAAT and provide zakat and through this promote good and prevent evil.
Allatheena in makkannahum fee al-ardi AQAMOO ALSSALATA…
42:38 they ESTABLISH THE SALAAT and their affairs are decided by mutual consultation
Waallatheena istajaboo lirabbihim WAAQAMOO ALSSALATA waamruhum shoora baynahum wamimmarazaqnahum yunfiqoona
Since all matters of the momineem are decided according to the permanent values of the Quran, surah Al-Airaaf has kept phrases like (tamas suk bil kitaab) and (aqamatis salaat) together in (7:170). It means establishing a society in which all individuals follow the laws given by the Quran and thus be attached to the book of Allah.
The basic issue in this discussion is that whether man should decide his matters of life according to his own wishes or according to the guidance provided by the revelation from Allah? To decide all matters as of his life using the Quranic Guidance is what establishment of salaat is. By bringing (aqamatis salaat) i.e. establishing Salaat and (itba-ijazbaat) i.e. following one's own desires opposite to each other the Quran has further elaborated.
It is said:
19:59 (After the messengers) people abandoned salaat and started follow their own negative desires.
This means that by following his own wishes man abandons salaat, and by following the permanent values of the Quran he establishes it.
---End of references---
QxP 7:170: Those who hold fast to the Book of God, and ESTABLISH THE DIVINE SYSTEM, We never squander the reward of those committed to social welfare.
Waallatheena yumassikoona bialkitabi WAAQAMOO ALSSALATA inna la nudeeAAu ajra almusliheena