It refers to the meat, and you can tell from the fact that there is an -a ending for the adjective, indicating the usage of partitive case. Partitive case isn't necessary when we're talking about one whole countable thing, like a chicken instead of meat from a chicken. If this were about one such animal rather the meat from it, there wouldn't be an -a ending for the adjective.
Plenty. Those are pretty much anything that can't be divided into units, such as "ilma", which means "air". An example of those that aren't inherently mass nouns is "olut", meaning "beer", which is technically a mass noun, but since it can be and often is poured into glasses, it often is treated like a singular when the beer in the glass is conceptualised as one beer rather than some beer.
One wonders if strange is such a terribly common word in Finnish. You seem to use it rather a lot, but I had to ponder a couple of minutes to recall the equivalents from Spanish and Italian, languages I know quite well. Does this show a judgmental tendency by the Finns or is it just high on a word list for Finnish teachers?