Yes and no. Bitrix24 Cloud is available in 4 subscriptions plans - Free (no fees), CRM+ (paid), Project+ (paid), Standard (paid) and Professional (paid). There are no fees - explicit or hidden - when using the Free subscription plan.
There are no additional or hidden fees for commercial plans, which means there will be no charges above your monthly payments if you use Bitrix24 with CRM+, Project+, Standard or Professional subscription plans.
There are, however, optional payments for your free or commercial subscription plans (e.g. VOIP / web telephony credits, SIP-connectors, additional online storage). Please see our plans and pricings page.