The number of databases allowed is determined by your host, and usually can be setup via your host provided control panel admin. If only one database is allowed, you can share stores via the one database AND keep them somewhat separated by using table prefixes. Table prefixes can be specified during the ZC install process.

Ex. abc_; def_; ghi_; and so on. Use whatever naming convention works for you.

The downside of sharing in this manner is that your clients will all have access to the same database. In a shared environment, this could be a security issue and there could also be performance issues. Best is still to use separate unique databases for each unique store.

As for the installs, just create a directory space for each installation then follow the instructions for installing Zen Cart. You might be able to create subdomains instead. That may work better for you.