The efficiency is low, why lower the voltage then increase it again? Just increase the lithium battery from 3.7V to 5V. Other effects should be minor.
It looks like you want to use a lithium battery to produce 3.3V and 5V at the same time. This is also possible and has no impact. Just consider the battery power capacity. Calculate the current or power used by 3.3V and 5V and estimate the maximum current of 3.7V.
Yes, it is necessary to have a 5V boost circuit of 3.7V to charge a cell phone, because generally cell phones have a 5V input.
According to the standard, provided that it is greater than 4.2. Anything above V can be used as a primary charging source. However, most current mobile phone power input standards use 5V as the input average, taking IC7805 as an example, as long as it is greater.greater than 5 V plus BE0. 7V or more (5.7V) You can provide IC7805 as the input power supply, but the load will reduce the input current, and the result is that the output cannot reach the standard 5V. The principle is not equal to the real, and. the real needs are greater. So basically your boost circuit is best to use 5V as standard.