Yes, you should get a mobile app as long as your budget is sufficient. A mobile app can give you additional benefits even you are owning any website.
No, native apps do not run on multiple platforms. Cross-platform apps would be your choice if you would like your mobile app to run on multiple platforms.
Yes, you can take native apps as long as you have specific features needed in your mobile apps or any features that it is not related from your websites. Otherwise, we do not recommend you to go for native apps.
We recommend you to get a native app because it is more affordable but if you like to go with mobile web apps, we can help you in developing a website and mobile web apps. For more information, you can check out more with our web design or contact us.