Much like answering a client's phone line, communicating with clients is specific to each particular client. During a handover with a client, included in the discussion is how best to communicate with that client.
The manner in which a VA communicates with their clients can depend on what type of relationship they have, if the client is very formal or informal, etc. If unsure keep it professional, courteous and helpful.
In this day and age there are numerous ways for a VA to contact your client, and them their VA - eg email, WhatsApp, Voxer, text, etc
Each client will have a preferred way of communicating with their VA.
The Head VA keeps their client updated on how many hours are used, and how many remaining, for the month. If at any point it looks like hours may run out prior to the end of the month, the Head VA must advise the client and obtain permission to go over hours. If permission is not granted, the Head VA and anyone doing delegated tasks must stop work. This way at the end of the month the client doesn't get a surprise and isn't happy to pay the over hours.
If we are passing on messages to a client it is via their preferred method of contact - eg WhatsApp, text, Voxer, etc.
Clients will have various daily/weekly/monthly tasks for their VA, but also some ad hoc tasks, which they will communicate via their preferred communication method. This may be via an EA@ email the client sets up for the VA, whereby this is "owned" by the client. These inboxes need to be monitored regularly so as not to miss any tasks. If the task is urgent, the client may WhatsApp, Voxer or even call the VA so it doesn't get missed.
Again this is per client preference. Some clients like to get acknowledgement that the VA has received the task (if not given via phone call), this can be by way of a thumbs up in WhatsApp for example. Some like acknowledgement of receipt, and confirmation that it has been actioned. Client preferences will be outlined at handover, and/or as the relationship progresses between VA and client.