This is quite the multipart and deep question. You seem to understand the basics but just in case, I’ll recommend this website as a good overview, albeit dated in terms of current ICs and BMS competitors.
http://liionbms.com/php/index.php
Chips
This is dependent on application. For small packs like the one you’ve drawn, there are a wide variety of chips available. For larger packs, Linear (LTC6803) and Maxim (MAX11081) are the two main competing suppliers of BMS solutions. They provide the most integrated solutions for multi-cell management. The main differences from smaller packs are the higher series voltages, daisy chain communication and noise immune signaling.
Techniques
In either case, voltage monitoring, temperature monitoring and active balancing tend to be the primary needs of a BMS. Other features such as redistribution tend to be less critical and often do not warrant the added cost and hardware.
Solutions
Unfortunately, even though nearly all BMS designs have the same goals, rarely is there an all in one solution. Solutions are based on number of cells, voltages (chemistry), tolerance for loss, communication method etc. These variables are not all standardized between one project and another. Furthermore, technologies keep changing. Linear is considering replacing CAN-BUS with shielded Ethernet. ADC accuracy is increasing. Sample rates are increasing.
The tried and true method is just simple active balancing. That is extra voltage on a cell is bled off resistively. Other than that, the rest of the system is a simple matter of reading all the cell voltages efficiently.
The Future
Eventually, we will see a more robust landscape with better standardization. Companies like Elithion or Nuvation are designing BMS solutions that are nearly drop in solutions. Chip designers are getting a better understanding of customers needs and have already sought to distinguish between the different types of li-ion needs based on different industries. This will mean that we’ll start only paying for features we need. Even battery cell manufacturers are standardizing cell types. For now though, any battery design remains quite customized.
Q: What is the reason Lithium Polymer batteries are limited to 1C charging?
A: They're not, at least not fundamentally. You can get 5C and 10C charging batteries from e.g. A123 systems. The reason batteries are limited on paper to relatively slow charging rates is to avoid internal hot spots, caused by a chemical-physical phenomenon that causes lithium chemistry batteries to discharge relatively evenly over their electrodes, but actually concentrates charging current to the areas that have the highest ion mobility. This is chemistry dependent; there are cathode materials that avoid this problem mostly and thus can charge faster. It's fairly specialty stuff though, and it is generally not a good idea to use chemical energy storage for rapid-cycle applications. I will come back to this later
Q: If I'm charging a Li+ battery for 90s at 1C, can I safely charge at more than 1C?
A: Most Li+ chemistries can safely charge up to 2C with a voltage cap, but with reduced lifetime. Not deeply discharging the batteries will alleviate this though, and then some. The cycle life of a battery increases at least tenfold if you discharge it at most 10% instead of 50%. Check with the manufacturer or datasheet to make sure though. If there is no datasheet, you shouldn't use the battery in a production environment anyway.
Addendum:
It's not a good idea to use a battery as a quick-cycle energy storage. Even with shallow discharging, especially high current batteries will only last you about 10 000 cycles. This is what (ultra)capacitors are for, especially if you are oversizing the battery anyway. The only downside to a capacitor is the ~10x decrease in volumetric efficiency compared to a battery. Without that problem, capacitors are much more suitable for quick charging and discharging. You can charge Maxwell's BCAP series within 15s, for instance. That's 1000 and 3000F capacitors, hundreds of amps. Besides, with large charging and discharging currents, your supporting circuitry and cabling will probably be larger than the power source anyway.
Also, it's generally a much better idea to store and use lithium chemistry batteries at the top of their capacity, near 4.25V. You get more power out of them for less current and you charge them faster with lower C-rating. Also their apparent internal impedance is much lower the 'fuller' a Li+ battery is.
Best Answer
2 1.8Ahr cells in parallel is the same as 1 3.6Ahr. Its called a 1s2p cell.
Sometime LiIon chargers stop charging after a fixed time. Something like the capacitry / charge rate * 1.5. So you might not end up with a fully charged pack after a single recharge.
Using a single cell LiIon batteries in parallel (with the same specifications and age) is generally acceptable.
When they are initially connected though, you need to make sure they're nearly at the same voltage. When connected the current flow will be I = (V1 - V2)/(ESR1 + ESR2). So long as I is less than the peak discharge and charge current you're fine.
If the batteries have the same specs, there is nothing more to worry about.
If the batteries are different (but operate over the same voltage range) then one just needs to make sure that during charging the current sharing doesn't violate the charge rate of 1 cell.
Even have a multicell stack, putting them in parallel is fine. But here it is a bit more tricky as the stack needs to be connected at the cell level, and the parallel capacity of each cell in the stack needs to be nearly identical.