Form kashrut.com (Footnotes in that article point to other references:)
All meat and poultry and their derivatives, even if no meat or poultry
is actually visible, e.g., chicken soup, are included. Pareve dishes
cooked in a utensil used for meat are permitted. [If a small piece of
meat accidentally fell into a pareve dish and its taste will not be
sensed, the dish may be eaten.]
Based on my understanding - the answer to your 1st question, about utensils is "yes", you can eat it.
While the 2nd question is not addressed, directly, it seems that since the oil is fleishig, the french fries are fleishig too, which MAY categorize in what is said in the 1st sentence regarding the chicken soup. There, even though there is no visible chicken, since a meat product, "fleishig" ingredient was used to make this soup, the soup is fleishig. So too, the fleishig oil was used to cook the french fries, and the french fries, even not having any meat itself, are considered fleishig. Again, my reasoning on this. Ask a good Rav about this. I'm curious, too.