Whoever this person is needs to appoint a qualified tax adviser. Very little of what you've posted makes much sense.
HMRC can't just look at your bank transactions. Banks report interest and investment income they've paid to you, but not the individual transactions on your bank account. HMRC can review the Land Registry to see if people own properties they haven't been declaring rental income / gains on.
HMRC can open an enquiry into a tax return, or lack thereof, and as part of that then request access to records.
If you have power of attorney you will be required to report back on every transaction made each year and its justification, but that takes places during the person's lifetime.
A gift, whether of cash or by paying bills, is not subject to income tax in the recipient's hands. It would potentially be subject to IHT depending on how many years prior to the donor's death it was made, unless covered by an exemption.
Bob's estate whilst in administration will have been required to file tax returns. Once the estate has been distributed to the beneficiaries then his daughter would be required to file tax returns reporting her income and gains.
As has been pointed out, if the estate was significant there will be IHT payable. If the administration of the estate hasn't been dealt with properly or HMRC has reason to believe there are inaccuracies in the IHT returns or her income tax returns, they could open an enquiry.
Whatever info you've been given is incredibly vague, inconsistent and quite confused to be honest. You also haven't mentioned timelines or whether probate has been granted, etc. So it's really hard to tell what on earth is actually going on.
Whoever this person is needs to appoint a qualified tax adviser to help them. If they have made a mistake it will not go away on its own. HMRC do not just give up and go away. And if they don't understand what they're dealing with there's a strong chance they could get themselves into deeper trouble. Depending on the taxes involved and the issue then there are penalties, some of which are behaviour based, as well as interest charges.
If they are on a low income, there is a charity called Tax Aid which works to help people on low incomes to resolve problems with HMRC, which has a helpline and may be able to assist. Taxaid.org.uk
However, if they have rental income of £6k pm(?) they won't meet the definition of low income (under £20k pa)... But it may still be worth trying the helpline depending on their actual circumstances. Their website is also designed to help people understand the tax system.
Whatever they do, they need professional qualified advice.