Can I file electronically when I have a W2 with income of zero? The W2 only has an HSA contribution. Can I delete the W2 but show the HSA amount on the federal form?

Yes, or if you are filing a W2 from that same employer, you can enter them both as one. 

I only have one W2.  I saw an answer to a similar question that said to change the income from zero to $1 so that that it would be accepted.  Is that a viable option for me also?

Yes, that would allow you to enter the amount, which would allow you to efile.