How to arrange indexes in MySQL with partition?

Question

MySQL

Table 1 (message table, binding by id_parent to the correspondence table between A and B):
`id` AUTO_INCREMENT
`id_parent` (binding to another table)
`text` Queries
used:
DELETE FROM `table1` WHERE `id_parent` = 1 AND ` id` = 1
SELECT ... WHERE `id_parent` = 1 ORDER BY `id` DESC
I want to create partitions by `id_parent` field.
If without partitions, then I would create the following indexes:
1) PK `id` (for the first)
2) `id_parent` + `id` (for the second query)
For partitions, you need to combine the AUTO_INCREMENT index together with the column to split, total PK: `id`+`id_parent`. Creating `id_parent` + `id` fails due to the error "Incorrect table definition; there can be only one auto column and it must be defined as a key".
Question: How to create indexes and partitions in this task?
A friend advises to create only one PK `id` + `id_parent`, and rewrite queries like this:
SELECT ... WHERE `id` > 0 AND `id_parent` = 1 ORDER BY `id` DESC . It seems to me that this is a bit of a strange crutch and it would be easier to create 2 composite indexes: PK `id` + `id_parent` and the usual `id_parent` + `id`.
Please help me figure out how to do this...
P.S. Volumes of operations per day: 400-450 thousand INSERT, 400-450 thousand DELETE, and several tens of millions of SELECT. Of course, I delete 1 time per day when there is no activity on the site.