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Yes, a physical quantity can have magnitude and direction but still be a scalar if it doesn't obey the vector addition. An example is Electric Current which has magnitude and a fixed direction, but it does not follow vector laws of addition.
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II)Cr2+ is reducing agent as its configuration changes from d4 to d3, when it is oxidized to Cr3+ .The d3 configuration have a half-filled t2g level which is very stable. On the other hand, the reduction of Mn3+ to Mn2+ results in the half-filled (d5) configuration which has extra stability hence Mn3+ acts as oxidizing agent.
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