tanin no kimoti wo rikaisuru.

の connects two nouns. Here it works like 's or of in English.

• 他人 = another person / other people
• 気持ち = feelings
• 他人の気持ち = other people's feelings or the feelings of others

So の shows that the feelings belong to, or are associated with, 他人.

を marks the direct object of the verb—the thing being understood.

In this sentence:

• 他人の気持ち = the thing being understood
• 理解する = to understand

So 他人の気持ちを理解する means to understand other people's feelings, with を showing what is being understood.

Japanese usually puts the main verb at the end of the sentence or clause.

So instead of English word order:

• understand other people's feelings

Japanese uses:

• other people's feelings + object marker + understand
• 他人の気持ちを理解する

This is one of the most important sentence patterns in Japanese:

• [object] を [verb]

Yes. 理解する is the plain dictionary form of the verb.

That means it is the basic form you see in dictionaries, and it can be used in:

• casual statements
• headings
• definitions
• subordinate clauses

Some common forms are:

• 理解する = plain non-past
• 理解します = polite non-past
• 理解した = plain past
• 理解している = is understanding / has understanding
• 理解できる = can understand

It is normally read:

たにん の きもち を りかいする

A few notes:

• 他人 = たにん
• 気持ち is usually read きもち
• 理解する = りかいする

So the full reading is:

たにんのきもちをりかいする

Yes—気持ち is the most normal modern spelling.

You will usually see:

• 気持ち rather than 気持

The ち is part of the word in everyday Japanese. Writing 気持 without ち is unusual in normal learner material unless it is:

• a shorthand style
• an incomplete kanji-only notation
• a formatting issue

So for study purposes, it is safest to learn this phrase as:

他人の気持ちを理解する

Not exactly.

• 人 just means person/people
• 他人 means other people, often with the nuance of someone else or people outside oneself / outside one's close in-group

So 他人の気持ち is more specifically other people's feelings, not just people's feelings in a broad generic sense.

Depending on context, Japanese might also use:

• 相手の気持ち = the other person's feelings / the other side's feelings
• 人の気持ち = people's feelings / another person's feelings
• 誰かの気持ち = someone's feelings

It can be, but it depends on context.

By itself, 他人の気持ちを理解する。 sounds a little like:

• a plain statement
• a goal or slogan
• a title
• part of a larger explanation

In natural conversation or writing, you often see it expanded, for example:

• 他人の気持ちを理解することは大切です。
  It is important to understand other people's feelings.

• 他人の気持ちを理解するのは難しい。
  Understanding other people's feelings is difficult.

So yes, it can stand alone, but very often it appears as part of a bigger sentence.

Japanese often leaves out the subject when it is obvious from context or when the sentence is meant to be general.

English usually needs a subject, but Japanese often does not.

So 他人の気持ちを理解する。 could mean things like:

• I understand other people's feelings
• to understand other people's feelings
• understanding other people's feelings
• a general statement about understanding others

The exact subject depends on context.

Yes, 理解する is grammatical and natural, especially in more formal, educational, or serious contexts.

However, depending on nuance, other verbs may also be common:

• 分かる / わかる
  more everyday understand
• 察する
  to sense / infer someone's feelings
• 汲み取る
  to grasp or read someone's feelings or intentions
• 共感する
  to empathize

So:

• 他人の気持ちを理解する = to understand other people's feelings
• sounds correct and natural
• slightly more formal or conceptual than 他人の気持ちがわかる

理解 is a noun meaning understanding/comprehension, and adding する turns it into a verb:

• 理解 = understanding
• 理解する = to understand

This is a very common pattern in Japanese, especially with words of Chinese origin:

• 勉強する = to study
• 説明する = to explain
• 連絡する = to contact
• 確認する = to confirm

These are often called する-verbs.

Yes. A very common way is to add こと or の after the verb phrase.

For example:

• 他人の気持ちを理解すること = understanding other people's feelings
• 他人の気持ちを理解するの = understanding other people's feelings

Then it can become the subject of a larger sentence:

• 他人の気持ちを理解することは大切です。
• 他人の気持ちを理解するのは難しいです。

This is useful because whole verb phrases can act like nouns in Japanese.