Please, explain strange behavior of connect by

You need the NOCYCLE because of the PRIOR statement.  Without the PRIOR, it doesn't really do anything.

The PRIOR you have creates a loop in the data. If you comment in the AND and remove NOCYCLE, you'll get an error:

ERROR at line 4:
ORA-01436: CONNECT BY loop in user data

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From the docs:
https://docs.oracle.com/en/database/oracle/oracle-database/12.2/sqlrf/Hierarchical-Query-Pseudocolumns.html#GUID-2F2FBA6F-2FD1-47D6-A74F-DB4B31E4D400

NOCYCLE enables Oracle to return the results of a query that would otherwise fail because of a CONNECT BY loop in the data.

>> can't understand why it leaves only 2 records of level 1 after uncommenting AND...

I'm not thinking it is just level=1.  It returns "if the current row has a child which is also its ancestor"

I got that phrase from the same doc link above for the CONNECT_BY_ISCYCLE Pseudocolumn .

You can see that if you add it to your query:

SELECT id,level n,ticket_cnt t, CONNECT_BY_ISCYCLE 
FROM(
	SELECT'aaa' AS id,2 AS ticket_cnt 
	FROM dual
		UNION ALL
	SELECT 'bbb' AS id,4 AS ticket_cnt
	FROM dual
)
CONNECT BY NOCYCLE
(
	level <= ticket_cnt
	AND id = PRIOR id
)
ORDER BY 1,2;

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All that said, are you sure it is returning what you want?  I've not been successful using a column value in a connect by level like that.  My guess is the PRIOR and NOCYCLE is because without them, the query generated a LOT of unnecessary rows.

Nothing further to add. I endorse Slightnw's comments.