So basically how can I charge both the cells without adding any more major components?
You severely underestimate the complexity of two-cell LiPo charging. A specialised IC designed for two-cell Lipo charging is recommended, as there is a complex sensing and 'balancing' process that needs to happen during charging to ensure both cells are changed at the same rate/voltage, else problems can occur.
A possible IC for charging 1,2, or 3 Cell lipo batteries is the Texas Instruments BQ24133 and similar devices. They have a large range of battery managment ICs, check it out.
arduino needs 7volts to operate.
Well that is not entirely true - it needs 7 volts because it has a crappy cheap linear regulator on the Vin input jack. It has a large drop-out margin, so needs the 2V gap between the 5V output and the 7V+ recommended input. You can bypass this with your single cell lipo by putting it directly into the VCC pin (V5+ pin). PLEASE NOTE YOU MIGHT DAMAGE YOUR ARDUINO, AND YOU CANNOT RUN THE ATMEGA328P AT 16MHZ ANYMORE!!
Basically, you will need to somehow get a 3.3V, 8Mhz version of an arduino (Like the arduino Pro [mini] with 3.3V 8Mhz setup on the board) and do what I mentioned above. Please be careful, there is no reverse protection or over-voltage protection on this pin, as it's assumed to be nicely regulated and protected by then. Don't say I didn't warn you!
(Or how can I power this setup?)
I suggest you just get a much larger capacity single cell Lipo pack and let the bluetooth module's integrated charger do it's thing. Nothing wrong with 3.7V. Also your 2-cell Lipo will need regulating down to 3.3V somewhere, so there is losses involved with this as well. You must check that if you will use a single cell lipo charged fully to 4.2V, if the system will not be damaged by this - check max ratings for all devices in their datasheets. Maybe you should look at getting a 3.3V LDO (low dropout regulator) and plug the single cell lipo into this, which will nicely drop out the system at 3.4~3.5V and remain very efficient the whole time.
I suggest a Micrel MIC5205 for that purpose I mentioned above.
There are benefits to doing high voltage (like lower input currents), for motor driving etc and avoiding regulation of those high current driven devices, but for a low-power embedded system I suggest just staying with a single cell lipo with high capacity.