For the last entry, I thought I'd do all remaining 10 as I find Lesson 6 pretty easy generally speaking. Much easier than は vs が anyway.
Exercise #21 to 30:
①：I think this is a good instance of @Toritoribe was talking about when he said to look out for verbs. Since the fire broke out from the neighbor's house, I'd go with から。
②＆③：まで＆に：When two blanks are right next to one another, it's automatically 「までに」
①に：I can't really explain it but I just know it's に。
②から：from Santa Claus.
①から：I think one of these two is wrong but I think this is a reason から.
②から：Since Japan sent a minister, it's the source. I think that's the one which is wrong.
So actually the first one was wrong, not the second one. Let's think about this some more.
The first particle modifies: 「今回のサミットミーティング」, a "Summit Meeting", which is an event. It's place where something takes place, which, in this case, is at the "Summit Meetings".
に is a particle I have trouble with. I'd say that's the particle I find the hardest to understand.
①まで：until this morning.
As expected, the difficulty ranks up in the last 5 questions.
①まで: until 横浜, so it's a straight up case of まで.
②から: I think this what @Toritoribe mentioned here, namely that てから means "after doing".
③に: destination of an action.
④まで: until ホテル.
⑤＆⑥：までに: same reason as before, see above.
⑦に：I think this also the same example @Toritoribe gave here.
**** yeah, perfect!
①に：point in time when something takes place (precise).
②から：the reason why the person has to be in the office by 8:30.
③＆④：までに：same reason as above.
I honestly hesitated between から and に here. I was aware that から was "from" here but for some reason the sentence structure confused me (which was probably the point).
①まで：I think "until" is implied here, as in "until" overtime. Not 100%, maybe it's から here however.
③に：place where s.t. or s.o. exists.
④まで：until 9 o'clock.
The answer key gives が as the first answer and it's not even one of the possible answer choice. The rest if fine though. That's about the third mistake I've spotted in the book. It's weird for a book which has been published for so long.
① に： destination. I was wrong here. After I went off-shore by boat is definitely a まで, as far as, spatial limit.
④まで：all the way to the bottom sounds like まで to me.
②&③: まで＆に by today.
④：に：direction of the action. I was wrong here. The idea is that you borrow "from" the library, thus から. The rest is good though.
①に：a place where a person exists.
②から: from the brother.
③に：indirect object of come.
④まで：study Chinese there until next summer.
⑤から: after studying Chinese.
⑥＆⑦：まで＆に：see reason above.
⑧に: destination with 帰る.
Wow, I got this one too!
I'm glad lesson 6 is finished as I thought it was on the easy side. Still I learned a lot of things by doing the exercise. Next up is lesson 7 which I'll probably start tomorrow or even today. We'll see!
Thanks for reading and @Toritoribe for his help!