No. You can apply for tax exempt status with your old EIN. It may be showing not “recognized” by the system because you may not already have tax exemption status.

There is no problem with conducting a 50/50 raffle or other prize raffles, either with prizes that have been donated or ones that have been purchased by the chapter.

No. You can be a tax exempt organization and have a portion of your dues go to lobbying expense as long as they disclose the percentage of dues that are non-deductible to the member. A portion of dues are not tax deductible to the member, but the chapter can still be tax exempt through the IRS.
A tax exempt organization does not pay tax on their income that is generated for their primary purpose and mission. They may pay tax on unrelated business income. They must go through an application process through the state and federal governments that grant them that exempt status.

You always need to report income regardless if you are tax exempt or not.

A 50/50 raffle is traditionally a fundraising event where attendees buy raffle tickets and a winner is chosen. The winner collects half of the pot and the other half goes to the chapter.

The Statement of Information (SI100) must be submitted every two years, regardless of your officers changing or not. The fee to submit is $20.00. The Secretary of State's website to submit is located at www.sos.ca.gov.

It depends on whether you have received your tax exemption status for your chapter from the IRS. If you are tax exempt, you will use the form 990 – if you are a C Corporation (corporation – not tax exempt entity) and never filed for exempt status, a form 1120 and form 100 should be used. C Corporation refers to any corporation that, under U.S. federal income tax law, is taxed as a for-profit entity.

It depends on the fiscal year that the chapter noted when they applied for non-profit status. The chapter will work with three entities for tax and filings. The three entities are IRS, State and Secretary of State. Both the IRS and State are tax filings and the Secretary of State requires a Statement of Information filing every two years.