Old English and Old Norse are mutually intelligible (especially after you realize the precise correspondences like un- = o-). Gunnlaugs Saga explicitly says the English and Norse are of one tongue and features a Norse poet singing to an English king. As another example, Ohthere of Hålogaland (Norway) visited King Alfred's 9th century English court and simply spoke to them in his own language:
> Whoever preserved this story was also curious about Ohthere’s descriptions of where the Angles had lived ‘before they came into this land’ (England). Members of Alfred's court remembered that their ancestors came from mainland Europe, and they wanted to learn more about the lands which they identified as their own places of origin.
The scribe explicitly wrote things like "he said krán which we call crein" showing they were speaking in their own languages. It's even clearer if you consider our standard Old English is West Saxon from 850 and our standard Old Norse is from 1250 in Iceland (more different than the Danish variety of most Scandinavians in England). At the same time point,they would have more similarities (8th century Danish had wír before w turned to v).
Anglo-Saxons not Dutch. But the short answer is yes. The word Welsh is derived from the Old English word for foreigner.
Latin would have been spoken in towns and cities but as Roman rule collapsed it was replaced by Brittonic (ancestor of Welsh), unlike in the continent where it developed into various Latin derived Romance languages.
