Sorry, but what has baby-led weaning got to do with periods and family planning...? Baby-led weaning takes a lot of patience and restraint to let the baby explore on her own rather than spoon-feeding puree directly.
As for periods, no one can tell. It is said that breastfeeding mothers get their periods later, but mine came around 5 months PP.
For your 2nd baby, it is really up to you, but the recommended time is 18 months for the mother's body to fully recover from pregnancy.
http://www.babycentre.co.uk/x555984/what-age-gap-is-best-between-babies
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Mommy of 2+1