Hosting and Setting Up Own Shiny Apps Without Shiny Server

Accessing Shiny App from the WordPress site

Yes, but you need to do more things before generating the link.

1. Using shiny::runApp directly is not recommended. You want to use a shiny server instead. Depending on the version (free, paid) you use, user counts, load balancing and other settings can be modified accordingly. I personally recommend to use shiny docker instead of installing by yourself.
2. Once your Shiny apps are running in a localhost port by the shiny server, In order to have it visible for people outside your local network, you need to use a reverse proxy service like nginx or apache to "export" to ports.
3. Setup your server firewall configs so reverse proxy service can pass the firewall.
4. Optional, go to your domain manager, create a subdomain for shiny apps.

Additional detailed readings: https://deanattali.com/2015/05/09/setup-rstudio-shiny-server-digital-ocean/

Back to your question
Q1, once you have done above, you should have the Shiny app link, and you can use it on your WordPress.
Q2, there is no user limit, it depends on how powerful your server is. Too many people using the server at the same time may crash it. Paid version of Shiny server has load balancing settings, not sure about the free version.

Can you recommend how to manage package dependencies for apps hosted on shiny server?

I was able to achieve this using adisarid's answer here:

Using renv:

log into the production server, get into the app's directory. Then run
R, and use renv::restore and then renv::isolate.

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