No. Handwrite roughly the 300 most common characters and recognise the rest. Native speakers write a few hundred by hand regularly and type the others via pinyin.

It still helps. Correct stroke order gives characters a consistent visual rhythm that speeds up recognition, makes dictionary and handwriting-input lookup faster, and shows you the components that dense characters like 警 or 餐 are built from.

Fewer times than most apps ask, but spread out. Trace a new character three times, write it from memory once, then review it the next day and the next week. Over 60 days that is 8 to 12 repetitions per character, which is what stroke memory actually needs.

Yes, just a different kind. Pen and paper gives better feedback on stroke direction and suits first exposure; a touchscreen with a stroke-order overlay gives instant correction and fits any spare five minutes, which makes it better for daily review.