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I m on EEA2 visa since 2014, unmarried, runs out on 2019, and I m with my EEA partner for 7 years now, but we will be breaking up soon, can I apply ILR after we inform home office about the break up ? I lived here more than 10years. Also I started a business this year, do I have to cease all business activities once we inform Home office about the break up ?

ILR is only for those who are resident under the UK Immigration Rules.

Unfortunately, as an unmarried partner of an EEA citizen you are considered to be an extended family member, without the same rights as a spouse.

See the official guidance below:

Termination of durable partnership
A durable partner continues to have a right to reside as a durable partner for as long
as:
 they remain in that relationship with the EEA national
 their EEA family permit, residence card or registration certificate remains valid
If the relationship is terminated at any point during the 5 years before permanent
residence, then the durable partner no longer has a right of residence.
Durable partners cannot keep a right of residence under regulation 10 on the basis
that the relationship has broken down, whether this is due to domestic violence or
otherwise. This is because regulation 10(5) only makes provisions for a family
member to retain a right on termination of a marriage or civil partnership. As a
durable partner is not in either a marriage or a civil partnership, regulation 10 does
not apply. This reflects article 13 of Directive 2004/38/EC.

What is your full UK immigration history?

You could apply for ILR long residence IF you meet all the requirements and have all the documents proving your partner has been a qualified person exercising treaty rights for the whole time you have been on a residence card as an EFM.

You also cannot have any period of overstay, i.e. last visa expiry and a gap possibly until your RC was issued.