Have you received an H1B RFE from USCIS?
As an H1B visa holder, your stay in the US is reliant on having H1B eligible employment. Should you decide to marry while working in the US, your immigration status will not change but there will be a number of related factors to consider, largely depending on the status and nationality of your future spouse.
Working in the US with H1B status, you will be required to pay tax on your earnings to the IRS. Your classification for tax purposes, and the level of tax that you pay, will be determined by whether you are a resident alien or a non-resident alien.