If I backup my iPhone to my computer, would it backup the apps there too?

For future reference:

A Finder/iTunes backup includes nearly all of your device's data and settings. However, it does not include any of the following items:

• The apps themselves.
• Content from the iTunes/Music and App Stores, or PDFs downloaded directly to iBooks/Books
• Content synced from iTunes/Music, like imported MP3s or CDs, videos, books, and photos
• Photos already stored in the cloud, like My Photo Stream, and iCloud Photo Library
• Touch ID settings
• Apple Pay information and settings
• Activity, Health, and Keychain data

Ref: How to back up your iPhone, iPad, and iPod touch with your Mac - Apple Support

No; they'll be redownloaded from the App Store as part of the restore process if they're still available.

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