Using the て form

Ok so I've just learned the て form using Barron's Japanese Grammar book. (Great book, but almost not worth reading since it uses exclusively romaji).
Here are a few sentences, I'll attempt to use the て form in a few different ways. Please let me know where my mistakes are, and how I can correct them

今は、食べ物を食べていません。
I'm not eating food right now.

私は、スーパーに行っていませんでした。
I was not going to the supermarket.

彼は、 水を飲んで、日本語を学びます。
He drinks some water, then studies Japanese.

I guess that's all I have for now. I think the first two are passable, but I'm not so sure about the third sentence. I heard the て for could be used to combine two actions in one sentence, so that was my attempt
Any criticism would be highly appreciated! Thanks!

In the second sentence, 行っていませんでした doesn't express the past progressive tense. It's more close to "didn't do at the time".

As for the third one, that's grammatically correct but sounds odd to me, since the present tense has a nuance of a habit that he ALWAYS drinks water before studying Japanese. If it's the past tense 彼は、水を飲んで、日本語を学びました, it's natural as a description of a scene.

Toritoribe said:

In the second sentence, 行っていませんでした doesn't express the past progressive tense. It's more close to "didn't do at the time".

Click to expand...

So how might I express the past progressive tense? Does a past progressive tense even exist in Japanese? How may I revise the sentence to match what I'm trying to say?

Toritoribe said:

As for the third one, that's grammatically correct but sounds odd to me, since the present tense has a nuance of a habit that he ALWAYS drinks water before studying Japanese. If it's the past tense 彼は、水を飲んで、日本語を学びました, it's natural as a description of a scene.

Click to expand...

My main purpose was to see if I used the て form properly. Thanks allot for the advice though, I'm glad you pointed that out. I've noticed that allot of Japanese verb tenses are approached with a slightly different way of thinking than they are in English.

First of all, you need to know the difference between ～ている form of continual/durative verbs(継続動詞) like 食べる and punctual verbs(瞬間動詞) like 行く. The former expresses "the present progressive" (is eating), whereas the latter is "the current state that results from prior movements" (went somewhere and is there now). For instance, 死ぬ(to die) is a punctual verb, so 死んでいる doesn't mean "to be dying". It actually means "to be dead (died in the past, and as the result of that, is dead now)", so other expressions like 死にそうだ, 死にかけている, 死につつある are used for "to be dying" instead. Similarly, I would say スーパーに行く途中ではありませんでした or like that for "I was not going to the supermarket".