The Tax Cuts and Jobs Act ended the penalty for not having minimum essential health coverage starting in 2019 (not for 2018). However, an individual without coverage in 2018 may be able to escape the penalty by claiming an exemption. Some must be requested from CMS; others directly on the tax return. Check the IRS website (https://www.irs.gov/affordable-care-act/individuals-and-families/aca-individual-shared-responsibility-provision-exemptions) for more details.
For 2007, a high deductible health plan is a health plan with an annual deductible that is not less than $1,100 for self-only coverage or $2,200 for family coverage, and with annual out-of-pocket expenses that do not exceed $5,600 or $11,200, respectively.