Formatting of your post is hard to follow, but will try to reply best I can as best I understand your question.

Yes, this is doable. Setup Field 2 to "Condition Self" and select Field 1 then select an operator and supply a value. Now setup Field 3 to "Condition Self" and select Field 2 then select an operator and supply a value. Now also on Field 3 add a second condition that's also "Condition Self" and select Field 1 then select an operator and supply a value the same as you did for Field 2, but set it to hide if the value isn't matched and set it to "One Way". This should give what you're wanting if I understand correctly; diagram as follows.

Field 2
Display: Field conditional self
Field: Field 1
Operator: Does Contain
Value: Animal
Mode: Show

Field 3 (Condition 1)
Display: Field conditional self
Field: Field 2
Operator: Does Contain
Value: Dog
Mode: Show

Field 3 (Condition 2)
Display: Field conditional self
Field: Field 1
Operator: Does Not Contain
Value: Animal
Mode: Hide
Direction: One-Way

Swap condition 1 and 2 on Field 3 and that might fix it as they condition in order.

QUESTION 1: IS CORRECT?

Yes, that'll do the trick too as it'll reset the dropdown so it needs to be re-selected and allows for the conditions to re-check properly.

HE QUESTION: 2
is it correct what it shows file conditional? See image file please

First issue is you have no Field selected. Second issue your value is not correct, you can not put a comma separated list. You'll need to use REGEX operator and supply a value of /value1|value2|value3/ if you want to check against multiple values in same field.

QUESTION 3:
How can add more than 5 conditions that it shows tab plugin?

You can't, 5 is the maximum.

QUESTION 4:
build a directory with three levels of categories nested.

Don't understand the question, you already have 3 levels of depth. Field 1 > Field 2 > Field 3.

there is a tutorial that shows this? I have not seen.

Nope.