Can I use this sign to mean a period of time?
No, this specific sign is used for the punctuation mark or to emphasize that a statement is final. For a 'period of time', you would use a different sign, typically involving the 'T' handshape moving in a circle over your non-dominant hand.
Is this sign used for menstruation?
No. The sign for menstruation (a woman's period) is completely different and usually involves tapping the side of the chin or cheek. This pinched-finger sign is strictly for the grammatical dot or emphasizing finality.
How forceful should the movement be?
If you are just talking about grammar, a light, quick tap in the air is perfect. If you are using it to say 'I'm done talking, period!', you can make the motion much sharper and more aggressive to match your tone.