Japanese sentence structure?

Question:

I've just began studying Japanese and what I've picking up so far is that the Japanese language appears to be 'missing' many words which in English, we would consider fundamental. Mainly the fact that they don't have words for is, it, a, the and plurals.
I know they have 'topic markers' and 'subject markers' and other particles like them, but I'm very confused by the sheer dissimilarity between Japanese and English.

For example, if you were to say, (and sorry I don't know where my Hiragana keyboard is??) that cat is cute. Would it be, sono neko ga kawaii, that cat cute?

Or I ran to school, (I don't have enough vocab to even attempt this) I school ran?

Or It was boring, would you just say 'Tsumaranai' because couldn't that also be it is boring?

Also Japanese people supposedly don't use pronouns such as I or you, once to topic of a conversation is established. But does that mean if half way through a conversation I wanted to say "Would you like to go shopping with me?" Would I end up saying 'would like go shopping???'
As you can see I am extremely confused and have a VERY limited (ie. non existent) vocabulary, and although I know both hiragana and katakana, I would probably find an answer easier to understand in just romaji.
Help would be really appreciated.

Answer:

japanese actually has an it is word which is desu pronounced des. my japanese is a bit rusty but i think your sentence would be something along the lines of sono neko kawaii desu