About the verbs in "there is" constructions:

I would not be so categorical in terms of "быть" for inanimate and "находиться" for animate objects.
Different options are possible, but each of them has its own semantic nuances.

1. A verb can be omitted altogether:

На столе лампа.
В саду мужчина.
Под столом кошка.
etc.

This construction is frequently used when you describe what you see right now.

2. "находиться" can be used with ANY nouns, but it usually sounds more bookish and formal:

На столе находится лампа.
В саду находится мужчина.

Although, I would not say "Под столом находится кошка" since it would be too formal for this context.

3. "быть" (present tense: "есть") can be used with ANY nouns. But let's consider nuances:

На столе есть лампа. - existence. It states WHAT exists on the table.

В саду есть мужчина. - Generally, it sounds as if the man exists in the garden permanently.

But in some context, it works fine. Imagine you are going to rob a house with your friends And one of your friends asks you:
- Посмотри, там никого нет? (Look (check) if there is no one there).
Then you CAN answer:
- Тихо! Там есть какой-то мужик. (Silence! There is a man there). Here, "есть" is fine, it underlines presence of someone as opposed to absence.

Note that "Там какой-то мужик" (without any verb) is possible too. However, the former version emphasizes presence (есть), and the latter emphasizes the man himself.

Под столом есть кошка. - Theoretically possible, but sounds a bit unusual. However, in some context it might work, too.

4. "лежать" - to lie (people or animals), to be in horizontal or in any random position (things):

На столе лежит книга.
На диване лежит мужчина.
Под столом лежит кошка.

5. "стоять" - to stand (people or animals on their feet). to be in vertical position or on a dedicated basement (things):

На столе стоит лампа. (If on its base)
На столе стоит стакан.
На столе стоит книга. (If on its binding)
У окна стоит человек.

6. "сидеть" - to sit (mostly people or animals)

В кресле сидит мужчина.
Под столом сидит кошка.

Note that 4), 5), 6) are extremely common in colloquial speech.

7. "быть расположенным" - to be allocated. Inanimate objects only, very formal.

На столе расположена лампа.
В комнате расположен диван.
В центре Земли расположено ядро.

8. "иметься" (more like "to be available", "to be in availability") - less formal, but still formal. Mostly used with inanimate objects. Can be also used with animate objects, but in some very specific context.

На столе имеется лампа.
В комнате имеются стулья.