へと is used when you are directing your audience's attention to the content that comes after the と for emphasis. 「やや強意の副詞的表現に属することを表す」
The white ball disappeared into the crystal clear blue sky
透き通るような青空の中 へ 白いボールが吸い込まれていく
Without the と it is simply a statement of fact.
Q: "What did the ball ...
The difference between using で and と is the difference between "we went out as a family" and "I went out with my family", I think of it as rather like the French "en famille". 家族で is very common expression and you can also hear this grammatical use when people refer to doing things as a group (グループで／皆でやりましょう).
It is another variation on the use of the で ...
I feel like this has been asked before, but I can't find it if it has. You've got it spot on with と being the quotation marker; that is Xと言う means that X was literally (more or less) what was said. Using を is more about the meaning/gist/essence of what is said. Here's a pair that I always remember to help distinguish them.
なにを言ってるのか？ → "What are you ...
Here is how I would categorize these usages. There are probably other ways to explain them, and I do not claim that mine is the best in any sense.
(1) ～ようと思う, ～ようと考える, and ～ようと決める are just the usual use of the particle と which signifies quotation, and there is nothing special about the combination of a volitional and と. For example, I think that particle ...
The quoting particle と (or って) is tenseless, just as the quotation marks " for direct speech (she said "I want to sing"), or that for indirect speech (she said that she wanted to sing) are tenseless.
The tense is reflected in the verb that is used with the quoting particle, e.g.
In your example sentence, the correct tense for ...
This type of って is mainly used to repeat one's opinion, like "I'm saying ～" or "I told you, ～". So it's still quotative in a sense; the speaker is quoting their own previous statement. For example, depending on the context, 「寝ろって。」 can mean either "[Someone] told you to sleep" (quote from a third speaker) or "I told you, go to bed!".
But って also often used ...
と has quite a few meanings. To name a few...
The case particle (格助詞) と can mean "and" or "with". It attaches to 体言, such as nouns and pronouns. eg:
「りんごとみかん」(apples and oranges)
「わたしと一緒に」(together with me)
The case particle と can also be used as a quotative particle. It attaches to almost anything, eg:
「おいしいと思う」(I think it's tasty) ...
This と is a simple quotative-と, and this sentence is a typical example of a rhetoric device called 転置法 (hyperbaton) or 倒置法 (anastrophe). This is very common in Japanese poetry/slogans/lyrics because the grammatical role of a word is mainly expressed by the particle type rather than the word order.
Does word order change the meaning of a sentence?
I think it can be replaced with は and というのは here, as in   at this Daijisen definition.
According to the 日本語文型辞典, this って indicates a subject, and can be an informal way in speech to state meanings/definitions or to add value/emphasis.
When used after nouns and adjectives to state meanings/definitions, this って can correspond with とは. When used after ...
This sentence says "(I) will be fired in no more than 10 days." (time)と待たずに is a common set phrase which literally means "without waiting for (time)".
This と is not "if" nor "then". The role of と here corresponds to the sixth entry of デジタル大辞泉's definition.
Originally, と was used after each word in a list. From here:
The last と in a list is usually omitted at least in modern Japanese. In this sentence, you can safely omit the second と, but explicitly putting the second と emphasizes that these two (それ and これ) are ...
What does the と in the sentence mean? Wouldn't 対象する work alone?
No, 対象する doesn't work alone (since 対象 is not a suru-verb).
ＡをＢとする (or ＡをＢにする) means "make A B", so クリーチャーを対象とする (or クリーチャーを対象にする) literally means "make a creature the target", "set/have a creature as the target," i.e., "Your target will be a creature."
Is there a simpler, less wordy, ...
Both 家族で and 家族と are correct.
で can sometimes mark an organization/group which makes some action, as if it were a subject.
It's the third definition on デジタル大辞泉.
東京外国語大学言語モジュール treats this as an extension of で as a location marker, as follows:
Yes these are different. There are (at least) three ways of using number + counter + と, and they have different nuances.
concrete number + counter + と + adjective
This is for showing a concrete figure before using an adjective like 大きい/短い/重い. Probably this is a kind of quotative-と. The number/amount can be big, small, or neither.
In Japanese, 彼の車は私と同じです is a perfectly natural sentence. When you compare two things, this type of omission* is extremely common in Japanese, and it can be found even in the most formal writings.
(* This may seem to be "omission" from the English perspective, but Japanese people may say nothing is omitted.)
His English is better ...
家族で should be taken as "as a family" rather than "with family"
(Both と and で could be used, though IMHO, 家族で implies that all family members were present whereas 家族と implies you only went with some/maybe all family members.)
The Tatoeba translation is a natural rather than a literal translation. Literally it's saying more like "I will have my sister go to the station by car to meet you". (迎える is a tricky little word that means to greet/meet someone, but often includes the implication of subsequently escorting them to their destination, so the "pick you up" element is also ...
As for your first sentence, you're right that the と is a quotative particle.
It's often used with a verb that introduces one's utterance or thought, e.g. 言う, 思う, 感じる, 知る, 分かる, 話す, etc.
A few examples:
痛いと顔をしかめる (「言って」「思って」 etc. are occasionally left out)
(examples above taken from 明鏡国語辞典)
You're right. The ～～なければ here is a shortened form of ～～なければならない and means "have to~~" "should~~". And 清らかな子供たち, それを無条件で愛する教師, and 尊敬すべきこのクラス are the objects of 信じなければならない. (This is an inversion/倒置 of 清らかな子供たちと、それを無条件で愛する教師、尊敬すべきこのクラスを、信じなければ。)