Today, a very surpriseding incident happened! Today, a very surprising incident happened!

This makes sense, but I think that "incident" usually has a slightly negative feel to it. Most people would probably say something like "today, something very surprising happened!"

Today, a very surprised incidenting thing happened! Today, a very surprising thing happened!

As fesgtep pointed out, "incident" typically carries slightly negative nuance. The generic "thing" will suffice here.

Today, a very surpriseding incident happenoccurred! Today, a very surprising incident occurred!

An incident usually describes something negative, it would be better to say something like "Today I had a very surprising encounter!"

When I went to shopping, I met a member of my dormitory unexpectedly! When I went shopping, I met a member of my dormitory unexpectedly!

Both "when I went shopping" and "when I went to the shops" would work.

When I went to shopping, I met a member of my dormitory unexpectedly! When I went shopping, I met a member of my dormitory unexpectedly!

Whilen I went toas shopping, I met a member of my dormitory unexpectedly! While I was shopping, I met a member of my dormitory unexpectedly!

(Just in case) for some context, although most of the members had comgone back to their homes, one of the members didn't. (Just) for some context, although most of the members had gone back to their homes, one of the members didn't.

I think "just in case" doesn't really fit here. It sounds like this person stayed behind for safety reasons or to be there for something in particular (e.g. it's often used in sentences like "he'll stay at home today just in case the delivery comes"). Based on what you wrote, I think something like "just for some context" would work better, since you're introducing some background information.

Just in casefor context, although most of the members had comgone back their home, one of (the members / them) didn't. Just for context, although most of the members had gone back home, one of (the members / them) didn't.

You can replace the second instance of "the members" with them to avoid repeating the phrase too much.

Just in caseto clarify, although most of themy dorm members had comve gone back to their homes, one of the members didm hasn't. Just to clarify, although most of my dorm members have gone back to their homes, one of them hasn't.

The one that hasn't is the person I met was her. The one that hasn't is the person I met.

She seemed to go shopping after she had finished her part-time job. She seemed to go shopping after she had finished her part-time job.

She seemed to be goingo shopping after she hadhaving finished her part-time job. She seemed to be going shopping after having finished her part-time job.

The tenses here are a little complex. However, the most important thing to note is that "to go shopping" should be in what we call the "continuous aspect": "to be GOING shopping". Actually, this is consistent with the native text: "買い物に来ていた" is also in the "continuous aspect" because of the "～ている" component of the conjugation.

SheIt seemed to gos she was going shopping after she had finishedgetting off work at her part-time job. It seems she was going shopping after getting off work at her part-time job.

While we went back the dormitory, I think she felt tired, she wasince she slept. While we went back the dormitory, I think she felt tired, since she slept.

While we wenton the bus ride back to the dormitory, I think she felt tired, she wasince she slept. While on the bus ride back to the dormitory, I think she felt tired, since she slept.

You should probably mention that you were a bus. I thought she was sleepwalking for a moment!

While we wentOn the way back the dormitory, I think she felt tired, she was she was so tired that she fell asleept. On the way back the dormitory, she was so tired that she fell asleep.

I think I'lld work until I was exhausted like her if I started a part-time job. I think I'd work until I was exhausted like her if I started a part-time job.

Since you're talking about something hypothetical, you should use "I would" instead of "I will".

I think I'lld work until exhaustedion like her if I stared part-time job. I think I'd work until exhaustion like her if I stared part-time job.

I think I'll be work untiling to exhaustedion like her ifwhen I staredt my part-time job. I think I'll be working to exhaustion like her when I start my part-time job.