Training for 3 month and attending conference is elegible under VWP?

Yes to Training, No to Internships

As you correctly point out, the Visa Waiver Program governmental webpage states:

Business

[...]

• attend a scientific, educational, professional, or business convention or conference
• attend short-term training (you may not be paid by any source in the United States with the exception of expenses incidental to your stay)

You should therefore be allowed to attend a conference in the USA on the Visa Waiver Program. You should also be allowed to complete a training period with a company in the US, as long as you receive no money from that company aside from reimbursements for living expenses.

More importantly however, a distinction is to be made on whether the training is considered an internship or not. The idea behind this being that internships can lead to a potential job offer, hence carrying out an internship in the US would effectively be considered job-seeking. This is specified in the Business Visa Travel to the United States leaflet which can be found on the aforementioned governmental website:

Training

Participating in a training program that is not designed primarily to provide employment. Will receive no payment or income from a U.S. based company/entity, other than an expense allowance or expense reimbursement related to traveler’s stay.