Use Web browser and Latex using iPad, Monitor, Apple Mouse and keyboard
For your use case, I'd advise to take a systematic approach starting with researching if the desired workflow is possible to be performed on an iPad end-to-end.

By end-to-end I mean getting data onto iPad, checking on the availability and maturity of the tools/apps which will satisfactorily get the work done and getting data off the device to desired output (digital such as sharing it with other computer/people or physical such as hard copy).

I'd try to address your concerns one-by-one as asked for in the question.

First of all, unlike a desktop computer or a laptop, an external monitor cannot be simply used as an extended display for an iOS device (iPad/iPhone). You can however connect your iOS device to an external display using an adapter to mirror your device. For more details, you can get started with the following Apple Support document:


About Apple Digital AV Adapters for iPhone, iPad, and iPod touch


If you would not like to involve dangling and always connected cable, a slightly expensive solution could be to connect an Apple TV to your display and mirror your iOS device using Apple TV onto the display.

While extended display is not natively supported by iOS, certain apps are programmed to take advantage of an external display and show extended content.

Coming to keyboard, it's possible to use external keyboards with iOS devices. However, your typical wired/IrDA wireless keyboard won't work. Bluetooth keyboards can be paired and work fine. Apple Magic keyboard can be paired to work with an iOS device. Various 1st party and 3rd party keyboards are available for iPad with iPad Pro supporting Apple Smart keyboard.

Using a keyboard frees up screen real estate. Using Apple Magic keyboard would be recommended in your case as you are planning to use an external monitor to mirror content. This way you can use the keyboard detached from the device.

iOS user experience is based on touch, not click and is not designed/programmed keeping a pointing device in mind. Hence it's not possible to use a mouse with iPad.

Google Chrome is available on the App Store and can be installed on iPad alongside Safari which comes pre-installed. You'll need to research on the availability of Latex apps on the App Store.