Learn Hardcore Japanese: watasi ha tuuti no zikan wo yoru ni setteisuru you ni site, youzi wo hiruma ni sumaseru. - I try to set notification times at night and finish errands during the day.

It adds the nuance of making a conscious effort or arranging things that way, often as a habit/policy. So 設定するようにして means “I make it a point to set / I try to set,” not merely “I set.”

Without ように, 設定して just states the action as something you do, with no “effort/habit” nuance.
Example: 毎日歩くようにしている = “I try to walk every day.” (effort/habit)

How is ようにする different from ことにする?

ようにする: “make an effort to/arrange so that …” (focus on ongoing effort or tactic)
ことにする: “decide to …” (a decision, either one-off or a rule you’ve set) Examples:
外食を減らすようにしている = I try to eat out less. (effort)
外食を減らすことにした = I’ve decided to eat out less. (decision)

Why is に used with 夜 and 昼間 (i.e., 夜に, 昼間に)?

With 夜に設定する, に marks the target value you set something to (and also works as a time point). You are setting the time “to night.”
With 昼間に済ませる, に marks the time when you finish your errands. Using で would be wrong here: 夜で設定する is ungrammatical in this sense, and 昼間で doesn’t mark time properly.

Why is there a に after よう in ようにする?

Because よう is a noun meaning “manner/way,” and the fixed pattern V-dictionary + ようにする literally means “to make it so in such a way that V.” For example, 忘れないようにする = “make sure not to forget.”

What exactly does 通知の時間 mean? Could I say 通知時間 or 通知の時刻 instead?

通知の時間: natural and conversational; context usually makes it clear this means “the time at which notifications happen.”
通知時間: compound-y/technical; can be read as “notification time,” but in some contexts can also suggest a duration. Avoid if you want to stress a clock time.
通知の時刻 / 通知時刻: emphasizes a specific clock time; common in UI/settings and the safest if you want “clock time.”

Why do we have を after 時間 and 用事?

They are direct objects of transitive verbs:

時間を設定する (set the time)
用事を済ませる (get errands done) Note the pair 済む (intransitive) vs 済ませる (transitive):
用事が済む = the errands are finished.
用事を済ませる = (I) finish the errands.

What does the …して、… connection mean here?

It’s the te-form link. It most often means “and (then)/and (also)” and can imply sequence or loose cause. Here it reads as coordination/sequencing: “I make it a point to set X to night, and (I) get my errands done in the daytime.”

Is 私 necessary? Could I drop it?

You can drop 私 if context makes the subject clear, which is very common: 通知の時間を夜に設定するようにして、用事を昼間に済ませる。 Use 私は when you need to mark contrast, introduce a new topic, or be extra explicit. Choice of 私/僕/自分 depends on formality and identity.

Why is the final verb 済ませる in nonpast/plain form? Is this present or future?

Japanese nonpast covers both present and future and is also used for habitual statements. Here it expresses a habitual policy. For a polite version, make the last verb polite: …用事を昼間に済ませます。 It’s also fine that only the final verb carries politeness; subordinate clauses often stay in dictionary form.

What’s the difference between 昼間 and 昼?

昼間 = “daytime” as a span (while the sun is out). Ex: 昼間に外出する.
昼 often centers around noon/midday or “day” versus “night,” and appears in set words like 昼ご飯 (lunch). If you mean the general daytime window, 昼間 is the clearer choice.

Can I move elements around, like 夜に通知の時間を設定するようにして?

Yes. Japanese word order is flexible. 夜に通知の時間を設定するようにして is grammatical and puts early emphasis on “at night.” The neutral/readable default is often “object を + target に + verb,” but fronting 夜に for emphasis is natural.

How would I make the whole sentence politely?

A common polite phrasing is to keep the subordinate clause in dictionary form and make the final predicate polite:

（私は）通知の時間を夜に設定するようにして、用事を昼間に済ませます。 Alternatively, you can also make the first clause explicitly habitual/politer:
…通知の時間を夜に設定するようにしています。

Could I use セットする or 決める instead of 設定する?

設定する is the standard/neutral “configure/set (a setting).”
セットする is more colloquial/katakana-ish and fine in everyday speech: 通知の時間を夜にセットする.
決める means “decide” and is okay in contexts like 時間を決める, but for device/app settings, 設定する/セットする feels more precise.

If I want to state explicit purpose, can I use ために instead of just linking with して?

Yes. For explicit purpose:

用事を昼間に済ませるために、通知の時刻を夜に設定する。 This reads as “In order to get my errands done in the daytime, I set the notification time to night,” making the causal relationship overt rather than merely sequenced.