I have several 18650 Li-Ion batteries, many with different capacities. Can I charge them with the same charging circuit (5 to 3.7 V 1 A buck converter)? Can I put them in parallel and use the same step up circuit to make a 5 V USB bank?
If you mean to charge each cell individually, then it should be fine, provided that the charger doesn't exceed max charging current for the smaller cell. But if you mean to make a battery out of two different cell in parallel, and charge-discharge them as a battery, then the following apply:
One should never charge different Li-Ion batteries in parallel. It is true even if the cells are of the same rating, but their charge-discharge characterics do not match to high (1-2%) degree. Charging cells in parallel is unacceptable for three reasons:
Li-Ion cells with different capacity will take different time because a smaller-capacity cell will/might be charged first, and then will be overexposed to charging voltage (while the bigger cell still gets the charge). This will result in "overcharging" of the weaker cell, it will grow some bad chemistry inside, its capacity will fall more, and it will die being bloated or worse.
On discharge cycle the process is also bad - weaker (less capacity) cell might be depleted first, and fall into "overdischarged" state, with similar bad implication for internal chemistry.
On charge, a stronger cell with less internal impedance might take more current than the cell design can afford, which can lead to "fast venting including fire".
In short, it is a very bad idea to make a battery from different Li-Ion cells in parallel without either perfect matching, or using some electronics to manage each cell individually.