Should the government mandate that large tech companies share their algorithms with regulators?

No, but if it's a threat to the common safety or the nation, then allow it.

Tech companies' algorithms have complex, unresearched effects on the people and should be monitored by independent teams that are staffed by a diverse set of people who have humanity-centered goals. Tech companies often do not consider the impact of their technologies on smaller, marginalized population since the nature of technology is creating benefits that increases the average person's life quality. Regulators of technology will have an almost impossible, but necessary role of safeguarding people's current life quality and striking a delicate balance between doing what is right (obligatory) and what is good (desirable, not necessarily obligatory). Companies should share their algorithms and methodologies on a case-by-case basis, as deemed necessary by the regulatory committee.

Only if the tech company is involved in weapons, artificial intelligence or security. In medical research, economic and social networks no

As long as regulators don't have any relations with competitor companies and they're also unable to trade on stock market

No. But if large tech companies are intentionally targeting minors, knowingly jeopardizing their health, they should be heavily penalized - a second offense should result in penalties so harsh they likely can not stay in business - and any awards won, should be distributed to programs which encourage minors to get out and exercise or play sports or anything NOT involving looking at a phone or tablet.