"We'll be coming back" refers to the proposed meeting at "half ten" (9:30) and says what the speaker expects to be doing at that time. (Future progressive tense.)
"We'll come back" states their return as a fact, and nothing else. You might use this if you don't know when or how you'll come back. (Simple future tense)
"We're coming back" is only slightly different from "we'll come back" in this context, but it makes it clear that there is a plan. (Present progressive tense) It treats the trip out and back as a single continuous action which is already in progress.
"*We'll coming back" is not English. Don't say this.
I'll answer these questions in reverse order:
3) Can I replace "I want to do this Improve..." with a better phrase?
Yes; improve is a verb, not a noun. Therefore, you should say, "I want to do this improvement..."
2) Can I use "have the intention of..." or it is supposed to use only in the negative form?
You can use this, but it's unnecessarily wordy. This time, you should consider using more direct language, by switching from the verb to the noun: "I intend to improve this paper"
1) Is the word "subject" appropriate here?
Perhaps, and perhaps not. All we know about these "subjects" right now is that we have two examples: "modelling" and "simulation." How are these referred to within your area of expertise? Are they subjects? Areas? Fields? Domains? A project proposal often uses specialized language, and you should use the term that is most fitting for your area of study.
Lastly, there's this:
I want these text to seem more sophisticated...
That's a bad goal, particularly if you're not a native English speaker. You should be striving for simplicity and clarity, not "sophistication." It's a gift to be able to write concisely without muddling up your text with unnecessarily complex words. You don't want to oversimplify your text – if you need to use a sophisticated word, then do so, but you should be doing that to make your message more clear for your intended audience, not just to add an element of sophistication.
Here's my recommendation, based on what I see so far (although I may be misinterpreting what you are trying to convey):
I intend to improve this paper by delving deeper into one of these 3 areas:
Best Answer
I think we usually say, "the rain was falling", or simply, "it was raining".
"Dripping" means a slow, intermittent process. If it was a very light rain, you might say "the rain was dripping". More often we say that a faucet is dripping, meaning that one drop falls every few seconds. Similarly, that water was dripping off the roof, or that you knocked the bottle over and the water was dripping out, etc.
You can say "the rain was coming down". Usually this is used for a very hard rain. "The rain was coming down hard" or "the rain was coming down in sheets".
I don't think I've ever heard someone say "rain was dropping" or "water was dropping". You can "drop" a bottle of water, but we don't normally say that water not in a container dropped. One exception that comes to mind is waterfalls: we say "this waterfall has a fifty foot drop", meaning, that's the distance from the top of the waterfall to the bottom. While we refer to individual units of rain as "rain drops", I don't think I've ever heard someone say, "the rain dropped".
If your ice cream is melting, you might well say, "the ice cream is dripping". If you said "my ice cream dropped", I think people would understand you to mean that the entire bowl or cone fell, not that small amounts of melted ice cream fell.
So to summarize: The common thing to say is, "the rain is falling" or "the rain fell". "My ice cream cone is dripping" or "The faucet is dripping" or "Water is dripping from the faucet".