Unfortunately, yes, if the USB 2.0 device seeks the USB-IF certification, it must obey the sequence 100mA -> USB_connect -> enumerated/configured -> full draw of port current. The "full draw" however should be determined by sensing the value of pull-up on attached CC pin.
If the attached cable is a "legacy cable" compliant to Type-C specifications, it should have 56k built-in pullup (you generally don't need any adapter, the cable has the pull-up).
If the attached cable is the "Type-C Standard Cable" connected to another Type-C port, the CC pull-up will be defined by the sourcing port, whichever it is capable of, 1.5 or 3A.
If you want your device to be practically charged, and charged faster, it is advisable to implement a battery-charging detector IC, at least to determine if the port supports Chinese-style charger signature, D+ connected to D-.
To really comply with USB-IF test specifications when using Type-C connector, you need to consult very carefully with this document, Type_C_Functional_Test_Specifications. This is an evolving area, so check for updates.
But if you don't bother with exhaustive USB-IF certification (as most manufacturers do), just take 500mA if it is enough for you, since every reputable host USB port must unconditionally support 500mA of sourcing (except nearly non-existing subset of low-powered portable gadgets running form tiny batteries).
No, the CC pins should not be tied together on Type-C receptacle. USB Type-C specifications, V1.4, has several places that deal with use of CC1 and CC2 pins.
If you are making a USb 3.x implementation, the active CC pin will tell you the right direction of Rx/Tx data MUX. Individual CC inputs on device receptacle form the entire idea of detection of plug orientation. The specs describe the process on p.165, Section 4.5.2.2.5.1 as:
If the port needs to determine the orientation of the connector, it
shall do so only upon entry to this state by detecting which of the
CC1 or CC2 pins is connected through the cable (i.e., the CC pin that
is in the SNK.Rp state).
More, on pages 162 and 163 the specs explicitly say, i.e. Section 4.5.2.2.3.1:
Both CC1 and CC2 pins shall be independently terminated to ground
through Rd.
Is this enough to convince you that CC pins should not be tied together?
Best Answer
If you do not want to support BC1.2 and high speed 480Mbps, you can ignore differential pairs of USB 2.0.