Regardless of whether you receive Childrens tax credits or not you can claim JSA or Income Support. If you were still receiving Working tax credits then that could affect a claim as that suggests one of you is working over 16hrs a week. but child tax credits do not affect a claim.
Couple rate is �92.80 per wk for JSA (income based) or Income Support, if JSA (Conts based ) is received this will be taken into account so over all that would be paid then made up to the �92.80 rate.
Tax credits are then claimed for children, obviously Tax Credits need to know your current circumstances to pay correct amount but full rate i.e non working family, is approx �45 per child, �16 family premium, �12 for a new born until 1st birthday. This is inlcuding Child Benefit overall.
I would imagine that when you claimed for the Income based part of Jsa, that perhaps the working tax credit was still in pay, hence the discrepency in the date your claim was paid from.
As a rule Jsa (income based) or Income Support cannot be paid alongside working tax credit. Also not knowing your circumstances, any other income you recieve can affect a claim as well. Hope this helps!