Can the same strand of DNA act as a sense strand and an antisense strand at two different occasions of transcription and result in two different proteins?
Yes, the DNA strand that is usually the sense strand, coding for the mRNA and protein sequence can also become the antisense strand if transcription happens in the reverse direction. This phenomenon called antisense transcription is a relatively recent discovery has been discovered to be quite pervasive in all types of organisms by sequencing all the transcripts in the cell, a method called transcriptomics.
Although the antisense transcript is usually a short non-coding RNA which plays regulatory roles influencing the stability of the sense transcript by it's complementary binding, in rare cases it can form a protein if it has the required site to initiate translation (ribosome bidding site) and the codons to make a protein.
These old papers from 1994 talk about antisense proteins - Do "antisense proteins" exist? J protein chem, 1994 Antisense overlapping open reading frames in genes from bacteria to humans Nucleic acids research, 1994