How do you calculate zakat on shares and mutual funds?

Your actual behaviour, not your self-description. If you buy expecting to sell within months on price movement, you are trading. If you buy expecting to hold for years and receive dividends, you are investing. A useful test: would you be comfortable holding this for five years if the price fell? If yes, you are an investor. If the whole point was the exit, you are a trader. Classify honestly and keep the classification stable between years.

It is an approximation of the proportion of a typical listed company's value that consists of zakatable assets - cash, receivables and inventory - rather than plant, property and equipment. Contemporary scholars accept it because a precise look-through calculation across a whole portfolio is impractical annually. It is guidance rather than a fixed rule, and it is worth adjusting if your portfolio is concentrated in a sector that is unusually asset-light or asset-heavy.

Yes. Zakat is assessed on what you hold on your zakat date at its value on that date, not on what you paid or what you have realised. If a holding has doubled, the higher value is what counts - and if it has halved, the lower value is what counts. Zakat is a wealth obligation, not a tax on profit, so realisation is not the trigger.