Actions in Sequence

I'm a beginning JP student (university level) and I had a chat with my Japanese teacher after class today about the -te form of verbs. She mentioned something about actions in sequence. I decided to play around with it for a few minutes, but now I'd like to know if I'm headed in the right direction with this.

夕ご飯を食べて、テレビを見ました。

How does the grammar look?

Can someone please help me go into a bit more depth with this concept?

Perfectly correct and natural.
The order of the clauses usually expresses the order of the actions. Thus, your sentence means that you had dinner first, and then watched TV.

The -te form itself doesn't have any tense, mood or aspect, so the meaning changes depending on the relation of the two clauses. For instance, in the sentence 夕ご飯を食べ過ぎて、お腹を壊しました, the -te form explains the cause why I have a stomach trouble. Probably you'll learn these things soon.

Thank you very much. Aside from this, the imperative use, and the -te imasu, what other uses does the -te form have?

Quite so many.
Wiki has some examples of the usage.
Japanese verb conjugation - Wikipedia, the free encyclopedia

In addition to these, giving/receiving expressions "～てくれる, ～てやる, ～てあげる, ～てもらう", a conditional ～ては (e.g. 腹が減っては戦はできぬ), indicating the means (e.g. 歩いて学校に行った), etc, etc.

Please be aware that the imperative use is actually just an abbreviated phrasing and is actually a request rather than an imperative (command). In terms of "feel" it probably strikes English speakers as a mild imperative, especially as the difference between imperative and request in English can often be the presence or absence of "please":

Hand me that book.
Hand me that book, please.

The distinction in the first case can be done by tone of voice, as to whether it is command or request.

Japanese uses different tenses:

お弁当を作って (下さい)。
お弁当を作って (くれる？)
お弁当を作って (もらえる？)
お弁当を作って (頂けますか？)
お弁当を作って (頂戴。)
Etc etc etc
Vs: お弁当を作れ for the imperative form

If using the actual imperative form, please make sure it is someone you are in a position to boss around. The negative reception this form can get is probably why foreign learners are taught that the abbreviated request form functions as an imperative; it's a lot safer (and there is no danger of choosing the wrong verb/form for the abbreviated bit).