炊く
This is 99% of the time be referring to cooking rice. If you try replace it with 作る and say ご飯{はん}を作る then the meaning becomes completely different, it means you will cook food in general, not rice.
As a side note, in some dialects 炊く
can mean to simmer.
For example 黒豆の炊いたん would be used in Kansai area.
炒める
You will often hear this as 炒め物, 野菜炒め, etc. because it is so common to take some vegetables and meat and fry them together.
For example, there are 466,677 recipes for 炒め物 on cookpad it is so common:
http://cookpad.com/search/%E7%82%92%E3%82%81%E7%89%A9
炒める itself you probably will hear on cooking shows or recipe books.
煮える
I don't hear this often as the transitive version 煮る since usually you are doing the simmering/boiling. Also, 煮物 is a very common dish, throw things into a pot and simmer them together.
I guess overall, you don't hear the above words very often in conversations unless you are into cooking (or actually cooking together with someone) and read recipes/watch cooking shows. However, you find the words pop up a lot in other words. For example ゆでる (boil) your hear a lot because of the word ゆで卵 (boiled egg) or 蒸す{むす} (steam) you hear in words like 蒸しパン or 蒸し{むし}野菜{やさい}.
However, 作る is the easiest to use when you aren't referring to a specific dish and say you are going to "make some food".
Also, if you are into cooking, Japanese has an abundant amount of words.
Here are some variations on 煮る alone:
・煮からめる
・煮きり
・煮込む
・煮立てる
・煮詰める
・煮びたし
・煮含める