Favourite bodyweight exercise and why?
I don't think there is any replacement for push-ups and pull-ups. These two exercises were the only thing that kept me in shape for a good three months or so during lockdown before some relief finally arrived in the form of proper barbells and stuff. But even after that, I do them every single day regardless of what I'm training on a particular day.
How to increase body strength specifically arm strength?
I can't speak for others, but the only thing that worked for me was lifting weights more than anything else, and doing lots of compound movements (squats, deadlifts, bench presses, shoulder presses, rows), bodyweight exercises (push-up variations, pull-ups) and explosive stuff (burpees, clap pushups, clean/squat presses with weights etc). You have to be sure to train every group i.e chest, back, shoulders, legs, arms at least once every week to gain proper strength, and your core/abs pretty much every day that you train. I cannot stress how important the last part is - not for getting a 6-pack or anything, but giving your body better balance overall which enables you to actually lift heavier thereby making you stronger. This is something they never taught me in my gym, but which I learned by watching several videos from channels such as Athlean X, V Shred etc on Youtube.
I would say make the first one i.e Athlean X your primary go-to channel when it comes to fitness; I don't know where I'd be if not for Jeff Cavaliere's home workout videos. As for something arms specific, check
this one (a bit advanced) and
this one. For an overall training plan for beginners, I would suggest
this one. And whatever you do, you need to ensure progressive overload over time i.e increase weight (by about 5 lbs/2.5 kg) or reps every week/2 weeks. It's a little difficult in the present climate with gyms shut, but there are plenty of alternatives to several of those exercises which you are unable to do at home if you don't have proper weights. One has to just search it on Youtube and try 'em out. I'm far from a gym expert myself, but that's pretty much how I roll now.
Also, don't try out any dumbass stunts such as lifting loaded gas cylinders and stuff - that's something I only did after around 3-4 years or so of proper weight training to the point where I could squat, deadlift, bench press all in excess of 100 kgs without much difficulty, and shoulder press around 75 kg. Doing so would only get you badly injured if you're just starting out and set you back even further in terms of your fitness journey.
Consistency and being on the park is the most important thing of all!