Can they raise fees AND charge late fee?

Yes they can, they can raise fees up to 20% under CA law without a homeowner vote and they can charge you late fees if you are late.

From davis-stirling.com:
20% Limitation on Dues
Notwithstanding more restrictive limitations placed on the board by the governing documents, the board of directors may increase regular assessments (dues) by up to 20% of the association's preceding fiscal year without membership approval. Civil Code §1366(b). To do so, the board must publish a budget in compliance with Civil Code §1365. Failure to do so means that any increase in the dues requires membership approval. Civil Code §1366(a).

Membership Approval. Regular assessments over 20% require the approval of a majority of a quorum of owners. Civil Code §1366(b). The statute defines "quorum" to mean more than 50% of the owners of an association. The governing documents of an association cannot increase or decrease the approval requirements for membership approval. Any such changes are voided by Civil Code §1366(b). Voting is done by secret ballot.

Thanks Bruce, I didn't do the math on the increase. I saw 10% and went with that figure. To the OP, Bruce is right any increase over 20% would have to be voted on and approved but if it was my original post stands, they can increase the assessment and charge a late fee.

Again from davis-stirling.com

Late Charges & Interest
As provided for in Civil Code §1366(e), regular and special assessments are delinquent 15 days after they become due (unless an association's governing documents provide a longer period of time). If an assessment is delinquent, associations may recover all of the following:

1. A late charge not to exceed 10% of the delinquent assessment or $10.00, whichever is greater (unless the CC&Rs specify a smaller amount).

2. Interest on delinquent assessments, reasonable fees and costs of collection, and reasonable attorney's fees, at an annual interest rate not to exceed 12%, commencing 30 days after the assessment becomes due, unless the CC&Rs specify a lower interest rate, in which case the lesser rate applies.

3. Reasonable attorneys' fees and costs incurred in collecting the delinquent assessment.

Authority to Collect. The authorization to collect late charges and interest need not be in the governing documents. Authority is granted by Civil Code §1366(e).

Fee or Penalty? Some try to argue that late fees cannot be greater than documented expenses to the HOA due to the delinquency. They use Civil Code §1366.1 to make their argument because the statute restricts associations from imposing assessments or fees that exceed the amount necessary to defray the costs for which it is levied. This fee restriction does not apply to late charges. Associations are allowed to charge a 10% fee regardless of the true costs incurred. That's because the "fee" is actually a penalty to encourage owners to be on time with their payments.