Yes in a charge you can move wherever you like as long as you don't enter ZoC, once you enter ZoC you must try to get into base contact. Once you reach base contact, a WE can
choose to continue to move, barging units as it goes, but it must still follow the charging rules - i.e. if it enters a unit's ZoC it must move towards it. However IMO there is nothing to force the WE to barge (or continue barging), it can stop barging (and thus moving) when it likes.
Likewise for counter-charges, the only difference is that you cannot choose the direction to move in. It still doesn't mean you are forced to counter-charge, or forced to barge if you do counter-charge.
However, this isn't the thrust of the OP - it is about whether you
can counter-charge if you are already in BtB. Normal units are not allowed to, and it's not because they are
fully engaged (2x units or the equivalent 2x DC), it's because they are in base contact. Dave I'm not sure what you are agreeing to - the need for an FAQ? Would someone please explain the logic of allowing WEs to ignore the first sentence of the counter charge rule

:
"Defending units that are not already in base contact with an enemy unit are allowed to counter charge."