переведите граммотно, пожалуйста) англ

Ну что же Вы, отвечающие! Просили же - с герундием! А он у вас не во всех предложениях присутствует. (Я уж не говорю об ошибках- пунктуация, выбор времён и т. д. А что такое it will throw one??? Кого выбросит кошка, по вашему? )
He admitted MAKING (HAVING MADE - после определённых глаголов можно брать как простую, так и перфектную форму герундия без разницы в значении) a mistake of not SUPPORTING his friend.
dj второй части больше подойдёт ПРИЧАСТИЕ, а не герундий - .a mistake NOT HAVING SUPPORTED his friend
NOT HAVING SUPPORTED - это причастие, а не герундий, without having supported - сказать нельзя, у причастия и герундия в отрицании разные функциии. У причастия - обстоятельства причины, а у герундия - сопутствующих обстоятельст.

You shouldn't undertake any actions without CONSULTING with their partners.
The cat dashed out of the doorway being afraid of BEING LEFT alone.
being afraid of - это опять-таки ПРИЧАСТИЕ, а не герундий, ГЕРУНДИЙ - BEING LEFT/ Поэтому чтобы избежать множества BEING, причастие лучше избежать, сделав придаточное предложение со сказуемым
The cat dashed out of the doorway because it was afraid of BEING LEFT alone.
Since the Minister for Foreign Affairs took the office he always insists on HOLDING //CONDUCTING negotiations.
It is possible to find A LOT OF various ways of IMPROVING education. = A lot of different ways of IMPROVING education can be found.

6. He recognized that has committed an error, without having supported the friend.
7. You shouldn't undertake any actions, without having consulted with the partners.
8. The cat has quickly jumped out for a door, being afraid that it will throw one.
9. Since the Minister for Foreign Affairs has held this post, he constantly insists on negotiating.
10. It is possible to find many various ways of increase of an educational level

. He admitted that he made a mistake by not endorsing his friend.
7. You should not take any action without consulting with their partners.
8. The cat quickly ran out the door, fearing that it will throw one.
9. Since the Foreign Minister took office, he always insists on negotiating.
10. You can find many different ways to improve education.
Thanks in advance. "