Carer's allowance (assuming you claimed it) is taxable but only if your total income exceeds the personal allowance.
The lump sum payments from your late husband's pension plans may be life assurance attached to the pensions. Usually, the payout will be the greater of the value of the pension fund or the life assurance cover. Either way, they aren't taxable.
You are entitled to a personal allowance for 2013/14 of £9,440 which means that the first £9,440 of your income will be tax free and you will pay tax at 20% on the balance. For 2014/15, the personal allowance will increase to £10,000.
In a full tax year, your income will be around £13,140 (£3,420 + £6,960 + £1,100 + £1,660). That's assuming you incur no expenses related to the let property. Take a look here
for information on the types of expenses you can claim against rental income.
As the tax office probably may not be able to collect any tax due on rental income through a tax code which would be operated against your pension, you ought to register for self-assessment using a form SA1
Your income for 2012/13 was probably less than the personal allowance of £8,105 so you should have no tax to pay for that year but it would be as well to check.
If you register for self-assessment, you will be sent your first tax return after 5 April 2014.
I hope this helps but let me know if you have any further questions.