Yes, and the two do different jobs. A booking platform is where an existing client rebooks. A website is what a new client finds when they search for a balayage specialist in your town, and it is where they decide you are worth the drive. The site should hand off to the booking platform, not compete with it.
Put them on. The salons that hide prices get calls asking for prices, and those calls interrupt someone who is mid-service. Publish per service, use from pricing where length and density change the number, and say plainly that a consultation sets the final price on corrective work.
We can, and we usually recommend against a live embed. Social embeds load third-party scripts that make a phone-heavy site noticeably slower, and if the account goes private or the widget breaks the gallery goes blank. A curated gallery you control, refreshed when you have new work, looks better and stays fast.
If your booking platform issues per-provider links, yes. We put the link on their page so a client who wants that person specifically does not have to hunt through a dropdown. If your platform does not, we set up the page to point at the general booking flow with the stylist named.
Builds start at $500 and are quoted per project depending on how many services, stylists, and locations are involved. Hosting starts at $15 a month and covers the SSL certificate, backups, and updates.