1.) Is it possible for me to use someone else's MacBook and iPhone to develop and deploy on the App Store? Are there any potential objections from Apple App Store?
From my experience, yes. I actually even build my app with a virtual machine, no objections from apple. I don't think they dig that deep into that.
2.) Are there any unforeseen challenges or complications that could arise from using someone else's equipment?
The availability of their equipment. Having to borrow stuff can be inconvenient for both parties.
3.) From point of using Construct 3, could I encounter any specific issues or hurdles in the process?
Nothing construct specific that I remember. Apple does vet the apps though and you might get rejected for various (annoying) reasons, which you then have to fix.
BTW, are there alternative methods or solutions for deploying apps on the Apple App Store?
Sites like macincloud.com but it's not exactly cheap.
Or the aformentioned Virtual Machine, if you're willing to go through some initial setup headaches.
You still 100% want a device to test on though. You can also test on an ipad btw. I bought one a few years ago just for that reason, but I don't regret it at all. It's useful otherwise too.