I was covered by a HDHP only for the months of April and May this year. Can I still make a prorated contribution today for this year?

if you were covered by an FSA  you probably can't have a HSA in the same year

Can I have an FSA and an HSA?

Generally speaking, you cannot have an HSA and a health FSA at the same time. An FSA is considered additional health coverage by the IRS and would disqualify an individual from opening or contributing to an HSA.

However, there are limited exceptions to this.

A Limited Purpose FSA (LPFSA) that only covers vision and dental expenses can be paired with an HSA. You may hear LPFSAs sometimes referred to as "HSA-compatible FSAs".

A Dependent Care FSA (DCFSA) that covers dependent care expenses that allow an individual to work or look for work is also compatible with an HSA because it is not medical coverage.

Also HSA-compatible but less common is a Post-Deductible FSA. Before you hit your minimum deductible for the year, expenses are limited to dental and vision only with this account. Once you hit your minimum HSA deductible for the year, you can use the money from the post-deductible FSA account for all qualified medical expenses