You are talking about two things:
If you say »Koche Nudeln!«, then this theoretically is the sort form of »Du koche Nudeln!« or »Koche du Nudeln!« (but both sentences are unusual). This is because in »Koche Nudeln!« there is no subject. The subject is »du«. (It's the same in English: The subject in »Cook noodles!« is the omitted word »you«.)
This becomes more clear if you use the polite form: »Kochen Sie Nudeln!«. Here you have to use »Sie« as the object, you can't leave it out.
But »Nudeln kochen.« is different. It is not a command. It is a suggestion or an advise. You are not forced to cook the noodles. But it would be wise to do so. It's up to you if you follow this instruction or not. In »Koche Nudeln!« you are forced to cook the noodles. You have no choice.
»Nudeln kochen« is a short way to say »Die Nudeln sollten gekocht werden.« (»The noodles should get cooked.«). So this is a sentence in passive voice. The subject is »Nudeln« and the grammatical agent (who is cooking the noodles?) is not in the sentence.
Comma or full stop?
Well, this is the same as in English. Also in English you have the possibility to join independent clauses with commas.
English is a foreign language to me, but I'm pretty sure that this is also correct English:
Cook noodles, slice ham, cut onion and tomatoes into cubes, roast onions in a pan.
It's just a way to express that this actions belong together and it sounds nicer because it is not so clipped. (Commands are short and clipped, but these are not military commands. It's a nice and friendly recipe.)
But you can also write this as separate sentences in German:
Nudeln kochen. Schinken in Streifen schneiden. Zwiebel und Tomaten in Würfel schneiden. Zwiebeln in einer Pfanne anbraten.
The difference is the style. If you use full stops, each sentence gets a little bit the character of a command because of is shortness. But the writer of this recipe isn't a military drill sergeant. He or she wants to talk friendly to the reader and so commas are the better choice.