1. Couldn't the Ming have kept Annam if they had simply thrown more manpower into the region? Or alternatively, the Tang manages to keep hold of Annam even in its decline.
The state was relatively centralized by the time that the Ming attempted to interfere, and the fact that it remained independent even after three invasions by the Mongols suggests that the Ming wouldn't have been able to fare much better. Of course, it was ultimately forced to pay tribute in order to avoid further incursions, but it remained politically independent, allowing the region to develop a separate identity for centuries after Chinese domination.
The problem with your second condition is not that the Tang couldn't keep hold of Northern Vietnam, but why
any of the numerous fragmented successor states would consider it important to retain the area when they were more concerned about achieving dominance over the other states.
2. What are the repercussions of northern Vietnam slowly assimilating into one of the peripheral regions of China?
It would take several centuries for Northern Vietnam to be fully assimilated, which would be extremely difficult, if not impossible, without butterflying away the Five Dynasties and Ten Kingdoms period. This era of fragmentation was possible at the time because each region had a roughly similar population and had access to about the same amount of resources, but this situation would not have held true after the coastal/river areas increased in population under the Song.
However, it would be highly unlikely for the Tang to remain centralized for more than three centuries, while Vietnam was part of China before the Tang because South China had never been fragmented among numerous states, such as the situation which occurred in North China, during the chaos between the Han and Sui.
Why did the Viet rebel more than say the Zhaung or the Miao or any of the other random ethnicities that the Han slowly assimilated over the centuries? I'd say it's probably owing to their geographic distance, but then China was able to win over Tibet, Mongolia, and Manchuria eventually, and those places were usually considered to be less core than Annam was.
Tibet was not fully politically incorporated into China until 1950, and still remains ethnically, culturally, and linguistically distinct. In the past, it was a tributary of the Tang, although it sacked Chang'an, the Tang capital, at one point, and was later governed separately from China under the Mongols. Tibet was a tributary of the Ming, and although it was politically incorporated under the Qing, it theoretically remained independent in practice, as large areas remained geographically hostile and/or sparse in population.
Outer Mongolia was under Qing control for a few centuries, but it remained unorganized and theoretically independent, similar to the situation in Tibet, and became politically independent after the Qing collapsed. Meanwhile, Inner Mongolia was not fully incorporated until the mid-1900s, as it was subject to Japanese interference, although it had become occupied mostly by Han Chinese due to the Qing's policies in order to curtail Russian incursion during the 19th century.
Using Manchuria as an example doesn't really make sense, as the Manchus invaded China Proper and established the Qing. In other words, Vietnam would have to swallow China whole in order for an adequate comparison to be made, which would be extremely difficult, if not impossible, considering that Vietnam decided to shift its focus south into conquering Champa IOTL. In this case, the Manchus were gradually assimilated into Chinese culture within a century or so after utilizing Chinese policies, and although Manchuria remained relatively free of Han Chinese until the mid-19th century or so in case of a Han Chinese resurgence, the large volume of migrations afterward due to fear of Russian encroachment caused the area to be essentially part of "China" by 1900-50. If Manchuria had remained separate from China Proper, however, and a population boom had occurred around 1700-1800 due to trading links, it would probably remain culturally and politically separate from China today.
Wasn't Annam also under Chinese domination for more than a millennia? I am surprised it WASN'T sinicized, considering what's happened to outlying regions taken over by China Proper like Manchuria and Xinjiang and Guangxi.
Again, Manchuria doesn't count because the
Manchus conquered China, not the other way around. Annam was also probably very "sinicized" by the time that the Tang asserted control over the area, which explains the abundant number of Sino-Vietnamese words, along with the lasting influence of Confucianism.
Meanwhile, the area roughly consisting of what is now Xinjiang (East Turkestan) was under military occupation by the Han, Tang, and Qing, but numerous native states in the region continued to maintain independence during other periods, and large areas still have a predominately Uighur population today. Guangxi is vague because it, along with Yunnan, was originally home to several native states in the region, such as Nanzhao and Dali, but was later absorbed into the Yuan, and the Ming attempted to retain control afterward. However, the natives continued to resist foreign incursions for decades, if not centuries, so the process was gradual. If the Mongols had not taken over the region, however, then it might have remained independent for centuries afterward, and possibly remain as a politically separate state today.