I read your question over an start thinking if these are the phrases you wanted to have, あしたなんですが、いちじかん　はやく　つきます。 たくさんのパソコンなんですが・・・ aren't they? In that case, second one could be a part of conversation like this; "So, what are the contents of the boxes you are sending by our courier service?" "They are many PCs...(Do you mind carrying such breakable things? etc.)" 「なのですが」is grammatically explained as follows; 「な」 adnominal form of 1) auxiliary of assertion「だ」　 or 2) adjective verb's last sound "da" 「の」particlle　（this often turns to 「ん」when talking） 「です」auxiliary of assertion 「が」particlle meaning "but" Is this phrase casual? →The original phrase なのですがis colloquial and not used, for example in an academic paper. It's written only when citing someone's remark. When it comes to 「なんですが」,「の」turns to 「な」in euphonic changes, and yes, we recognize it as a sort of "casual down" or "a friendliness" or "more natural" way to pronounce the phrase, but still it's never too bad for any formal occasions like office meeting or formal party speech. For example, when writing an interview article of someone, interviewee might have actually pronounced 「なんですが」in speech, the writer would chose to put it 「なのですが」on paper if he/she want the article to sound not too casual, for example when the interviewee is a professor explaining about his research and want to sound professional. To be used only among friends? →No, it can be used in almost any scene as long as it is spoken. When put on paper as citation of someone's remark, you need to decide what level of casualness you want to present to the readers. Some examples of なんですが usage; Q: 「来週、一日　休む　件（けん）なんですが、何曜日ですか？」About the day off you are taking next week, which day is it? A: 「火曜日なんですが、だいじょうぶですか？」It is going to be on Tuesday, is it ok for you?

Hi Phillip, For the first thing, the example sentence you are giving is not grammatically correct. One I can guess its meaning but the other I can't. (I'm a native speaker of Japanese.) It's also difficult to presume what mistake the writer made (like, mistook the word with something similar, etc.) Where did you get them from? Especially the word なんですが　is wrong. This word does exist, but we don't use it like this. Let me translate word by word. あした tomorrow は (particle) なんですが、　(?) いちじかん one hour はやく early つきます。 arrive The subject is hidden but it's "I" from the context. Without "なんですが" it means, I will arrive one hour early tomorrow. たくさん many の(particle) パソコン PC は (particle) なんですが。。。 (?) This one does not make sense and I can not guess what the person wanted to say. Maybe I can guess the original meaning if you let me know where you got these sentences from.

Sorry, one mistake. ×　「の」turns to 「な」 ○「の」turns to 「ん」

Oh actually the sentences should be using -は particle

It's used to confirm that you have understood the question. A:　明日は？ B:　明日なんですが、一時間早くつきます。 B is just confirming that he has heard the question regarding "tomorrow." This is standard in Japanese, and considered very polite! You should make a habit of it.