Please check my English sentences.

Yesterday evening, when I got off the train, it was bucketing down outside.

I had no idea (I didn't think) that it would (it was going to) rain today. ('that' is optional and fairly unnecessary in this sentence).

As I didn't have an umbrella, I was (had to queue) in a long line to buy it (one) at a convenience store.

Better: As I didn't have an umbrella, I had to queue in a long line at a convenience store to buy one.

But (even with my new umbrella),  I got soaking wet on the (my) way home.

But (even with my new umbrella), I was soaking wet by the time I got (arrived) home.

Here is a correction based on US-style English:

Please check my English sentences.

* "It was coming down in buckets" or "the rain was coming down in buckets" is how we would say it in the US. If you said "bucketing down" people would probably understand, but it's not a normal American expression. 

** Both versions are correct. "I didn't think [that] it would rain today" is more common, but "I had no idea [that] it would rain today" is better to show that you were surprised. (In both versions, the word "that" can be dropped).

*** "As . . ." is fine. But I think most US speakers would say "Since I didn't have an umbrella . . ." (傘がないので濡れてしまった). You can also say "Because I didn't have an umbrella . . ."