I have read that you can contribute money to a Health Savings Account
even if you are no earned income. It that right?
Correct, there is no minimum earned income requirement to contribute to an HSA (source). However, with no income there's nothing to take the tax deduction from and you can't carry that deduction into future years. Therefore you would be missing out on any tax savings from the contributions (assuming they were made outside of payroll deduction).
I can transfer the money in a Health Savings Account into my IRA
without any tax consequences
Not correct. You can not transfer from an HSA to IRA, but the reverse is allowable (IRA to HSA). However, this transfer can only happen once and must be less than the annual maximum contributions including any personal or employer contributions. You must also be eligible to contribute to the HSA for 13 months following the transfer. Failure to do so will incur income taxes and penalties.
(Source from 53.com, under Frequently Asked Questions)
EDIT: Here are the IRS rules regarding IRA to HSA transfers, from Publication 969:
Qualified HSA funding distribution.
A qualified HSA funding distribution may be made from your traditional IRA or Roth IRA to your
HSA. This distribution can’t be made from an ongoing SEP IRA or SIMPLE
IRA. For this purpose, a SEP IRA or SIMPLE IRA is ongoing if an
employer contribution is made for the plan year ending with or within
the tax year in which the distribution would be made.
The maximum qualified HSA funding distribution depends on the HDHP
coverage (self-only or family) you have on the first day of the month
in which the contribution is made and your age as of the end of the
tax year. The distribution must be made directly by the trustee of the
IRA to the trustee of the HSA. The distribution isn’t included in your
income, isn’t deductible, and reduces the amount that can be
contributed to your HSA. The qualified HSA funding distribution is
shown on Form 8889 for the year in which the distribution is made.
You can make only one qualified HSA funding distribution during your
lifetime. However, if you make a distribution during a month when you
have self-only HDHP coverage, you can make another qualified HSA
funding distribution in a later month in that tax year if you change
to family HDHP coverage. The total qualified HSA funding distribution
can’t be more than the contribution limit for family HDHP coverage
plus any additional contribution to which you are entitled.