Grammar – Can ‘In’ Be Used Instead of ‘At’?

The literal sense is...

plate - a shallow, usually circular dish, often of earthenware or porcelain, from which food is eaten.

It's not always possible to classify any given item as a plate or a bowl, but the general principle is that plates are flat surfaces, so food (or anything else) goes on them. In contrast, bowls are (also usually circular) containers with raised sides - capable of holding liquids such as soup, which goes in them.

Thus OP's example usage #1 is what we would normally expect when describing the spatial relationship between the forks and the plates.

But note the figurative sense #2 in my link - the contents of such a dish; plateful, and consider this

"Someday, I hope you'll mean that," she replied, sticking her fork in his plate for a quick taste.

As a native speaker, my natural inclination is to interpret OP's second example in terms of that second definition (she sticks her fork into the food on his plate, in order to help herself to some of it).

TL;DR: Things are usually located on plates (including the figurative "I had too much on my plate already to take on another task" as per the idiomatic sense 34 in my link above). Usages such as "Lindsey stopped eating and set her fork in her plate." are relatively uncommon, so native speakers may well look for an alternative interpretation to explain/justify the unusual preposition.

Without negation, does is used to question the truth of a statement, or to add emphasis. For example:

Does she use the wheels? Yes/No/I don't know

In your example, you're not asking about whether someone uses the wheels or not, but who uses the wheels, if anyone does at all. For instance:

Who uses the wheels? I do/she does/Alice does/Bob does

Does can also be used for emphasis in certain variants of English (US, UK, Aus, Canadian). For example:

Alice: "She doesn't use the wheels."

Bob: "Who does use the wheels?"

In this case, the use of does would be accompanied by a pitch movement, to show emphasis, usually with it being pronounced with a higher pitch than the rest of the sentence.