Even contributary ESA can be affected by a private pension. The DWP will discount the first £85 per week and then reduce ESA by 50p for each extra £ pension. So, in your case it will not make any difference
Contributary ESA is counted as taxable income, so you will be obiged to pay tax if your total (taxable) income is over the personal allowance threshold.
Edited to add - it is easier for us if you keep all your queries in one place please, rather than starting a new thread with each one. You will be able to find 'your' thread/topic easily if you mark it as a favourite now