Yes. If you have a health savings account (HSA), your contribution to a self-only plan is permissible up to set annual limits (in 2019 it’s $3,500, plus $1,000 if you’re age 55 or older by year end). Alternatively, if you have a dependent under the HDHP, you can contribute to an HSA up to the limit for family coverage.
Generally, the receipt of cash or its equivalent accompanying an exchange of property. In a tax-free exchange, boot is subject to immediate tax.