How to read names?

Are there any rules to read kanji's in Japanese names, be they people's or places' in terms of 訓読み or 音読み?

Some kanji's in dictionaries have 名乗りreading. Are such readings where available for names only?

Do all Japanese names come with kanji's? If not, are they written in hiragana or katakana?

What about Chinese characters in Chinese names of people and places? Are they always read in one of the 音読み sounds?

Almost no rules, which makes pronouns one of the most difficult things to nail down.
Nanori are for names only, but there are probably a ton of exceptions.
A lot of Japanese use just hiragana in their names. It is less common, but not out of the question, to use just katakana in names. It is possible to have a name that uses hiragana and kanji （みち子 for example)
For place names, usually yes, but there are exceptions where the pronounciation is based on a historical pronounciation rather than the Japanese onyomi of the kanji. The city of Hong Kong is written as 香港, and in Japanese it is pronounced ホンコン, but ホン is not an onyomi of the kanji 香. Beijing is written as 北京, but is pronounced in Japanese as ペキン, but ぺ is not an onyomi of 北.
For personal names or last names, it depends. For personal names, the pronounciation may try to replicate the original sound, as opposed to using the onyomi. Or, there may be a kanji used in a name that doesn't exist in Japan, and so the Japanese will again try to use the sound closest to the original pronounciation.

I've gotten used to a lot of names in Japanese, but I've accepted I simply won't master them. People in my age group (over 30's) tend to have fairly consistent names, but in the younger generation, parents really wanted unique names or more often, unique kanji. Often, I'll see a name in kana, and I know it, but trying to input the kanji on a keyboard takes me a few minutes because it's not the traditional kanji for that name. So I have to input the name one kanji at a time, searching each character. It's a pain in the butt, and this year I started just using katakana if it took more than a minute or two.

Thanks guys for your inputs.

Majestic said:

Nanori are for names only

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Is it for people's names or for places' names or for both? How nanori is used, I wonder.

It seems to me that the names of all the big places like 日本, 本州, 九州, 北海道 and 東京 and so on are mostly read in 音読み, but smaller places like 横浜 and 沖縄 seem to read in 訓読み. I wonder if names of Japanese places used to be read in 音読み years ago, hence older names in 音読み and less old names in 訓読み. I've been trying to find some rules or consistency so that I can remember more easily how to say them. It looks like I have to bite the bullet and learn to remember them one by one.

I've just found Chinese names in Japanese and I think it is quite informative. Toritoribe-san said the following.

Toritoribe said:

As for Chinese names, it's usually read in on'yomi especially for historical persons,

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I suppose it applies to modern people too such as 習近平.

Toritoribe said:

But recently, 習近平 is sometimes read "Shī Chinpin".

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He hasn't commented on name of places in China though.

nahadef said:

I simply won't master them.

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That makes two of us. I just let repetition and immersion help settle them in my memory one of these days. Owing to the irregularities in pronunciation of names, I don't usually put in extra efforts to remember how to say the names. Unlike vocabulary of daily use which I try to memorise the pronunciation first and writing later but I would try to remember the words of names in writing first and take care of the pronunciation later.

This is a name that I've only seen once--on a server's name tag in a restaurant: 卜

(うら)