How is the royalty rate determined?

How was 20 years decided for patent lifetime? This is an implementation detail to be argued about to find a fair formula.

How are cheap to manufacture/replicate inventions handled? With a low royalty rate the inventor may not recoup costs for a valuable patent.

Again, this is a matter of determining a fair mathematical formula that rewards inventors appropriately depending on the amount of sales.

Also, for comparison how does our current patent system ensure that inventors recoup costs on valuable patents? How does our current patent system reward downstream inventions and ideas? You seem to have lofty goals for a new system that our current system doesn't address.

How are products with multiple patents handled?

Again, implementation detail, but if multiple ideas contribute to the same product then the inventors of both would get rewarded.

How are patent fees enforced?

What patent fees? We're talking about taxing products / services / corporate profits and then using that money to reward inventors.

Why would a company publish a patent in your system? They can be 1st to the market and be the only ones in the market until their competitors reverse engineer their patent.

Because 6 months later when it's reverse engineered any competitor will be able to recreate it. If your idea is so unique and complex that you don't think it can be reverse engineered then fine, keep it as a trade secret, that's already how our current system works.