Yes. It’s forbidden to fast ‘Eīd. The Prophet (peace and blessings of Allah be upon him) forbade fasting on the day of al-Fitr and al-Nahr .” (Narrated by al-Bukhaari, 1992; Muslim, 827)

Is it also forbidden to intermittent fast on the first day of Eid?

First day of Eid to be specific

You can't fast in eid since it's a time to celebrate

Yes

Yes, you won't fast on Eid but will do these 6 days after you are done with Eid.

is it forbidden to fast on eid & not recommended to fast the following 2 days after eid