せいで

The word せい means act, doing or deed but in the below context it means 'fault' or 'cause'. The usage is entirely subjective and refers to the speaker's opinion about the cause or fault of something or someone. For example;

彼女とショッピング・センターに出かけたせいで、サッカー試合を見られなかったよ。
I was unable to watch the football match, because I took my girlfriend out to the shopping centre.

夕べ食べ過ぎちゃったせいで、今朝気に悪いんです。
I am unwell this morning because I ate too much last night.

Generally the indication is nearly always negative. Offering an explanation for a negative occurrence.

はもちろん

If we understand the meaning of もちろん to mean 'of course', we can understand this grammar point. For example;

日本の料理と言えば、寿司はもちろん、焼き鳥も焼きそばもとうふとがある。
If we talk about Japanese food, there is of course sushi, as well as yakitori, yakisoba and tofu.

The はもちろん starts the sentence with something expected by the reader or listener as a given example, either through context of something or something which symbolises the topic overall. To use it effectively, the first example should be something easily aware to the audience and then the use of Nも to describe other such things.

きっかけ

きっかけ can be generally translated as the 'trigger' or 'impetus' for a desired action or feeling. きっかけ is a noun.

日本語を勉強しているきっかけは、日本に行って、その経験は気持ちだった。
The reason (trigger) that I am studying Japanese is that I went to Japan and it was a pleasant experience.

ながら

When you began beginner Japanese all those many moons ago, you remembered ながら as something symbolising 'whilst doing something'. The meaning here is roughly the same and carries the same nuance in English.

イギリスは小さい国ながら（も）、色々なきれいな所があるし、歴史的な協会がある。
Whilst England is a small country, there are various beautiful places and historic churches.

The grammar is sort of similar to expressing the same thing as でも、のに、けど etc but it appears to be more of a fancy way of constructing things. The も is often included in written speech rather than spoken. I think the usage is the same in English and is perhaps a slightly formalised way of saying things. Anyway its good to know.

おかけで

Simply, 'thanks to' or 'owing to'... Again, like きっかけ it is treat as a noun. For example,

友達の支持のおかげで、お酒を飲むのをやめた。
Thanks to the support of my friends, I quit drinking alcohol.

もともと

A useful adverb and probably more helpful when you see it in kanji = 元々. This means 'originally' or 'starting from'

もともとは大学で中国語を勉強していたが、毎日アニメの番組を見たおかげで、どんどんお宅になって、日本語を勉強することにした。
Originally, I was studying Chinese at university but, thanks to watching anime programmes everyday, I steadily became an otaku and decided to study Japanese.