Using the TP4056 to charge a LiPo battery and supply power to my circuit
This is several questions and should probably be broken apart, but nevertheless


According to this TP4056 datasheet, a 1.2 kΩ RPROG will give a charging current between 950 and 1050 mA. This is a bit much for a lithium-ion battery, which typically prefers a charging current no more than 1 C (e.g. 900 mA for a 900 mAh battery). If you have a datasheet for your battery, it should say the recommended maximum charging current. You might want to go to 0.5 C (450 mA) to reduce battery aging. A 1.43 kΩ resistor would give a current below 900 mA, and a 3 kΩ resistor would give one below 450 mA.
The output of a switching regulator like that is typically fairly well-regulated (hence the name “regulator”). There are some graphs of the line and load regulation on this MT3608 datasheet.
You almost certainly do not need or want a linear regulator on the output of the boost regulator, as it would reduce the efficiency and therefore battery life a lot. The only common reason to add a linear regulator to the output of a boost regulator is to reduce the output noise, but the only really noise-sensitive component you mentioned is the XBee, and it will need a little 3.3 V regulator anyway (and feel free to use a linear regulator for that).
It looks like that USB port is directly connected to the Vin hole, so you can't connect USB power while a battery is connected, or you stand a good chance of exploding the battery. USB is already 5 V nominal, though, so you don't need to connect it to the input of the boost regulator—you can just disconnect the boost regulator and hook USB power up directly to your circuit.