Electronic – Different capacity lithium polymer batteries in parallel

Connecting cells in parallel is common practise with professional battery pack manufacturers, so there is nothing wrong with it. What pros do is they assemble packs from cells out of the same box (same shipment, same lot), having very tight tolerances. This way, you even get packs with serially connected cells (eg. 3s1p) where the cell voltages stay closely matched over the lifetime of the pack (several years) - without balancing of course. This is quite a considerable achievement, you can calculate yourself how much self discharge difference the cells can have in order not to have significant unbalancing.

Your case is much simpler (1s2p) so I guess you are using low quality cells. The above is only valid for top quality cells (Panasonic, Samsung etc), a lot of "noname" cells like used in aftermarket camera batteries are just crap. Which cells are you using?

A1. The built-in protection for li-ion cells should be considered "emergency protection"--it should not be relied upon for normal cycle V & A protection. In a "safe" battery design, V&A protection should "always" be included in your design.

A2. A thermistor protected battery system is wise. Sometimes li-ion cells do not dis/charge at the same rate & cause an imbalance in the series/parallel configuration of larger Ah batteries. A thermistor can be used to detect an overheating condition, prevent a fire, slow the dis/charge rate/s, or indicate a dis/charging fault in a smart battery system. I consider it very important in a safe battery system, but, it is often overlooked or ignored when ICR type li-ion cells are used. If you want to make a safe battery pack, then I suggest you always include a thermistor & supporting circuitry--don't allow the incomplete/shoddy designs of others to affect your design decisions.