Blesta uses the Portal/CMS plugin to create a landing page where clients can go to access their account, the order form, or the support system, etc. You are using the BlestaCMS plugin, which I am not familiar with, but it most-likely overrides the default Blesta Portal plugin. AFAIK you can create additional front-end pages with the BlestaCMS plugin though. You may want to ask @Blesta.Store for some help with that setup.
As for Blesta, it is not meant to replace your website, although you could use it that way, such as through a plugin like BlestaCMS. Any integration with Wordpress or another third-party platform will likely require modifications to the code to get it integrated into your particular site. There are some threads on the forums that describe how to do that if you're interested. However, Blesta is usually used on a subdomain or in a sub-directory of your website. If your website is at "domain.com", you might install Blesta at "domain.com/billing/". You can then update links on your website to go to "/billing/" to access Blesta-related content like the Order system at "/billing/order/" or client login at "/billing/client/login/".
Regarding packages in Blesta appearing on an Order form, this is something you can configure after you create your package in Blesta. Under "Packages > Order Forms" you can create a new order form and assign any packages you want to sell through it from the list of packages you have already created in Blesta. A link will be shown to access that order form directly. However, you can also set a default order form under "Packages > Order Forms > (Settings) tab". The default order form will be shown when accessing "/order/" in your browser. I hope that helps.