Part 1:
1a) 日曜日は図書館に行きます。
1b) 日曜日に図書館に行きます。
Are both natural. But mean slightly different things. Context is very important here.
Particle は is used to mark a topic of the sentence, or/and to contrast things. It is important to note that it is sometimes hard to say in which way は is used. What is the topic? It is simply something we are going to speak about. AはB. B has some kind of connection with A. Like the topic set on internet chats. It has to be said that the topic has to be the thing we assume other person knows something about, and of course we know about it too. So it cannot follow words asking for information. Because as stated before, both parties have to know the thing. If we ask “who?” it means we don’t have the information. So は never follows だれ、なに etc. This part will be also important when が and は will be compared.
On the other hand, に which(in this case, because it has a multitude of other uses) is simply used to point time expressions, “on Sunday”.
一月にポーランドに行きます。“in January”.
１９：３０に映画館の前で彼女と会います。“at 19:30”
The best way is to look at the problem from a wider perspective, the sentences will answer to different kind of questions.
日曜日はどこに行きますか。
日曜日は図書館に行きます。
Where are you going on Sunday?
(as for)On Sunday, I will go to the library.
Both parties know about which Sunday they are talking about. Maybe it was mentioned earlier? Well, that’s another story.
A:（ｂさんは・Cさん）いつ図書館に行きますか。
B:（わたしは・Cさん）日曜日に図書館に行きます。
When are you going to the library?
I am going to the library on Sunday.
As you see, unlike は it can be used to provide new information. It simply states on/in/at the time without additional nuance. As you noticed, the topic of this conversation might be either B san, or some other person©.
Ohh, and another thing, は can be added to other particles, retaining its function. So there is には、では、とは。Though those have more functions, and it is another story.
2a) これがこの町で一番高いビルです。
2b) これはこの町で一番高いビルです。
Like before both sentences are natural, everything depends on context. Ohh, natural if used with で.
で is used for location of places where some action/event takes place or something is in some state.
に expresses where something exists or not. It is used with specific words like ある、いる、住む、勤める、立つ。Etc. So you can say これがこの町にある一番高いビルです.
There are some special uses though, if に and で are used together in one sentence, the で will be attached to place that is bigger.
この町で大学に喫茶店がある。
In this city, at the university, there is a cafeteria.
And as I wrote, で can be used with ある/いる and others if there is some event taking place.
ロシアでオリンピックがあった。
In Russia, Olympics took place.(Olympics - event).
- As we have learned before, は cannot provide new information. It cannot follow だれ、何 etc when asking for new information. However, が can introduce it. It marks a grammatical subject.
女の人が(providing new information)スーパーに行ってオレンジを３つ買った。そのあと女の人は(setting it a topic, the information was already provided something like A and THE in English)２つ食べた。いくつオレンジは残っている？
- (If you have knowledge about grammatical cases, then you can think of it as an analog to a nominative case. The particles are called 格助詞(case marking particles in Japanese), and ガ marks nominative, の genitive, に dative, を accusative etc…, by the way, が was originally marker for genitive).
- は cannot be used in the subordinate clause(including relative clauses, which are subordinate clauses EXCEPT being used as contrast marker), while が can(and の can be used instead of が in this case too IN CASE OF RELATIVE CLAUSES).
[私が/の好きな]ゲームはこれ。Relative clause.[]
[子供が迷子になったら]、警察に電話をかけなさい。Subordinate clause. []
- There are some words that always appear with が(すき、きらい、ほしい、たい(though たい can appear with を too, mentioned ある and いる)etc)
- は can be used when talking in general about something, が is more specific
- Like mentioned before, は has a contrastive function, が doesn’t.
- Like mentioned before は can join with other particles, making it とは、には、では etc. が cannot
- There might be very slim connection of a sentence to a topic.
Lets again help ourselves by asking what questions those sentences would answer:
どのビルがこの町で一番高いビルですか。
これがこの町で一番高いビルです。
Which building is the tallest in this city?
This building is the tallest building.
As you see, we lack information about what kind of building is the tallest. The new information is provided with the particle が。
このビルはどんなビルですか。
これはこの町 で一番高いビルです。
This building, what kind of building is it?
This is the tallest building in the city.
Both speaker’s know about which building they are talking about. This is the topic, and some related information is being asked for and provided.
) are not related linguistically so what can be accusative in your language, doesn’t mean it will be accusative in Japanese. However, it works well pretty often and it is a solid base. Though from time to time you will have to learn with which particles verb works together with