Assuming you are below pension age all savings are ignored up to £6000 (total for the couple). From £6000 up to £16000 savings are treated as earning £1 per week for every £250 of savings & this amount is taken into account as income in working out the entitlement. If savings are £16000 or more then no HB/CTB.
Do not forget the minimum a couple are expected to receive each week is £209 so if your joint incomes from all sources do not add up to this you can claim pension credits
No it hasn't. not all rates are increased with inflation. Before the figures went to £6K & £16K they were £3K & £8K. They were then doubled in one go so the powers that be probably then thought they could stay unchanged again for years.