What are these crispy bits on top of rice?

Those are fried onions.

They're pretty recognizable, but for confirmation I did a search by image and found this blog post in Finnish containing that exact image. The caption underneath the picture is:

Kun riisi on kuohkeutettu, sipulit lisätään mukaan - n. kolmasosa jätetään koristeeksi.

Google Translate translates that to "When the rice is loosened, the onions are added, the -. The third of the leaves for decoration." I think the proper translation is probably something like:

After fluffing the rice, the onions are added, one third as garnish.

The recipe itself says:

Sekoita mukaan 2/3 paahdetusta sipulista. Tarjoa suurelta vadilta lopuilla sipuleilla koristettuna.

Which translates to (again with a bit of fixing):

Stir 2/3 of the fried onion. Serve on large dishes garnished with the remaining onions.

(Google Translate thinks "paahdetusta" means roasted, but earlier in the recipe it's pretty clear that the instructions are to fry them.)

You ask about things that look like those but might be smaller. I'd assume they're still onions, just sliced smaller (or possibly shallots) since that's a fairly common garnish. Of course, it's certainly possible you've seen something else; hard to say without a picture of the exact dish you wanted to ask about.

It looks Asian food. (I am Asian)
We (burmese) eat this in the morning as a breakfast, to literally translate "si-hta-min" => "Rice with Oil".
It was made by fried bean oil and cooked the rice in it. The cooked oil might have already included fried garlic.
We simply take it out before putting rice into it. And after the rice is pretty golden and cooked, we place the fried garlic over the rice as decoration.
Note : The beans/peas can add either while frying rice or after.

My answer to the question is "Fried onions/garlic". Whether it's garlic or onion is based on your meal choice, some people don't like garlic, while some does.