Does Peter’s vision in Acts 10 correspond in some way to the account of Noah in Gen 6?
I just taught on Noah and the flood this past Sunday. I do think that very often the New Testament writers had Old Testament texts and concepts in their minds as they wrote their works. Having said this, some is very subtle, and may or may not be apparent. I think when the connection is important, it will be obvious and emphatic. To more subtle the connection, the less important I believe it to be.
Regarding the statement that “object” can be translated “vessel” (as in boat), it can, but in 23 appearances in the New Testament it seems to be used of a boat only once, in Acts 27:17. As to the “sheet,” this term is used only twice in the Bible, in Acts 10 and then in 11. Nowhere is it used as a sail in the Bible, and this would seem to be an unlikely option for translation in the text you have mentioned.
About the “6 men” who were with Cornelius. It was about the 6th hour when Peter began to pray (10:9). I don’t see that number applied to people. Three were sent for Peter, and there were a good many more gathered at his house. All this would suggest that the number 7 would not play into this.
There seems to be one serious problem with your conclusion, in addition to the fact that you have to “reach” a bit with the “vessel” and “sail.” For one thing, Noah’s ship was not a sailing ship. But the biggest problem is that it was not the Noah and the Ark incident that gave Peter his revulsion to eating unclean foods, it was the Law of Moses. In fact, after the flood God gave Noah and his descendants permission to eat any animal, clean or unclean (Genesis 9:3-4). The distinction between “clean” and “unclean” animals was made at the flood, but this was not a distinction that related to eating, but only to the sacrifices (8:20).