Salamun Alaikum,
RESPONSE TO QUESTION 1:
There is an 'implied' historical context alluded by 'li kulli ummatin' (for every community / nation) and a present context contemporaneous to the Prophet's ministry.
Historical context:
This is first supported by the narratives of the previous verses which refer to the ancient rites that were instituted by Prophet Abraham (22:26-32). These were instituted for all the nations / communities that existed at his time and subsequently, to all those that followed after him. It was simply a proclamation to mankind ‘wa-adhin fi’nasi…” (and proclaim to mankind …)
Therefore, the verse ‘inherently’ captures all the nations that have existed from the time of Prophet Abraham to the time the verse in the Quran was being narrated during Prophet Muhammad’s ministry.
This is the historical context.
Present Context for Prophet Muhammad:
If verse 22:34 is read with 22:67, where the near identical phrase appears "likulli ummatin ja'alna mansakan" (For every nation / community, We have appointed /given rites), it is clear that the reference is also a localised one. This is clear from the context of verse 22:67.
There were undoubtedly communities that were still following the rites instituted by Prophet Abraham at the time of the Prophet. This could also be a reference to those Arab Jews and Christians that the Quran refers to as being on the correct guidance.
007.159
"Of the people of Moses there is a section who guide and do justice in the light of truth."
Summary:
There is a present context and an implied historical context which the phrase ‘li kulli ummatin’ captures.
RESPONSE TO QUESTION 2:
With regards the dominating of 'deen', I take it that you refer to verses 48:28 and 61:9. In verse 48:28, the context is clearly specific if read in light of the preceding verses. This is clearly a reference to the point that the 'religion of truth' (dini-lhaq) would prevail over all 'false' religions. The 'false' (as in false religion) is strongly implied as a contrast to the word 'haq' which is used in the same verse. The messenger was sent with the true religion to prevail over all false religions. That was his specific mission and indeed from the Quran itself, it appears he certainly succeeded with God's help. This has nothing to do with today and you are correct that it is primarily a reference to those contemporaneous to the prophet and in his general vicinity.
In verse 61:9, again context is important. The specific context becomes apparent when one reads "walaw kariha l’mushrikeen" (although the idolaters dislike it). So once again, it is a prevalence of the 'truth' over falsehood at a specific time during the Prophet's ministry over a specific people (mushrikeen). Again, as a primary purport of the verse, it has little to do with today as you quite rightly intimate.
I hope that helps, God willing.
Joseph.