Let me start with your second question,
So, my second question would be on how I can properly understand the googletranslate translation, whether it is right or not, and whether there are any better alternatives or not.
For the sentence,
I knew that you were/are an angel.
the google translation you got,
is correct. It's a natural Japanese expression. Other possibility will be
You can omit '私は' (and in fact it's more natural to omit it).
You can change '知っていた' to '分かっていた', and the meaning will be the same.
In the last expression, you can replace 'ことを' with 'ことは'.
Now let me address this part:
Finally, the last part, いた, has me lost, to be honest.
Basically, '知っていた' and '分かっていた' mean '(I) knew', i.e., to '知る' and to '分かる' in the past. Grammatically, the past tense of these verbs are '知った' and '分かった', but these emphasize the action or event of knowing something in the past. In other words, it is closer to "I got to know that you are an angel (at that time)." or "I realized that .. (at that time).", rather than "I have had the knowledge that you are an angle (since that time)." The part 'いた' adds this sense of continuity. '知っていた' is made of the words '知る'+'て'+'いる'+'た', and they mean 'to know'+'(and)'+'to be'+'(past)', or 'have been (or was) in the state of knowing', or 'have had the knowledge', which is usually expressed more simply as '(I) knew (something)' in English.
Next, let me address this part:
Furthermore, there is no te form or sentence chaining involved here - From what I get, こと converts the whole previous verb into a noun, so now we have this huge "you're an angel" - noun?
Yes, 'こと' makes the huge noun. Here it makes the noun clause, 'the fact that you are an angel'. The word 'こと' means 'fact', 'thing', 'event', etc. I think that the correspondence between 'the fact that ..' and '..こと' holds quite generally, and that it is useful to remember it.
Now, we need to talk about this part:
I get that "あなたが天使である" includes the "being/are" meaning of the sentence, while I above only ended with "です". So the difference in meaning when using desu and aru would be my first question.
To make the noun clause corresponding to 'the fact that you are an angel'
from 'あなたが天使です' and 'こと', we need to conjugate the (auxiliary) verb 'です' to the noun 'こと'. Probably the conjugated form of 'です' to continue to a noun is also 'です' (i..e, the same as the form to end the sentence), but for some reason it's rare to hear 'ですこと' (except in the cliche of a snobbish madam exclaiming something, as far as I can imagine). Instead, people start from a different expression 'あなたが天使である' and 'こと'. The noun conjugation form of '(で)ある' is again '(で)ある' (i.e., the same as the ending form), and the combination becomes 'あなたが天使であること'. So, to answer your question, there is essentially no difference between です and (で)ある in the meaning, but the latter is a preferred form when conjugating with a noun including こと. In addition, です is the polite form while (で)ある is the regular form. [You can make a polite noun clause as 'あなたが天使でありますこと' by changing (で)ある to (で)あります.]
Next, let me address this part:
Finally, my last question is about sentence chaining in general: How do we know what part comes first? Assume my translation above was correct for a moment, instinctively I put the "I know" part first. But I can see that in fact, the know part should come last as it is the true verb of the sentence. What about more complex sentences? And finally, why would the following be wrong/unnatural: 君は天使でして私は知りました
Generally, a Japanese sentence ends with a verb. Examples are:
- I know something. -> 私はsomethingを知っている。
- I run. -> 私は走る。
- I throw a ball. -> 私はボールを投げる。
- I speak Japanese. -> 私は日本語を話す。
- I am an angel. -> 私は天使である。
The reason why your sentence '君は天使でして私は知りました' is wrong/unnatural because it does not reflect the semantic structure that '(the fact that) you are an angel' is the object of the verb 'know'. To reflect the meaning correctly, you need to make a noun clause out of 'you are an angel' as explained above.
Now, instead of making the noun clause as 'the fact that ..', you can make a noun clause simply as 'that ..'. This corresponds to '..と'. For example, the sentence 'あなたは(が)天使だ' can be made to a noun clause as 'あなたは（が）天使だと' and then can be connected to a verb. Another example is
- She said that she is 129 years old. -> 彼女は、(彼女は)129歳だと言った。
In this way, you can avoid inserting 'the fact' when it distorts the meaning that you want to deliver. To conjugate to 'と', the preceeding verb should be in the form for ending the sentence. So, you can literally take one sentence and throw it into another one.
Finally, let me address about combining sentences with 'て', which was your initial target of practice. Examples of using 'て' are
- I run, and she walks. -> 私は走って、彼女は歩く。
- It's dark, and it's dangerous. -> 暗くて、危ない。
You can generally combine two senteces with 'て' when they are combined by 'and' in English.