Unspliced XBP1 protein is relatively unstable. So most cells do not have high levels of the unspliced form. However, upon ER stress, TLR stimulation and in secretory cells IRE1 is activated and splices mRNA of XBP1 producing the spliced XBP1 (sXBP1) protein. This protein is relatively stable and detectable by Western blotting.  PBMCs have detectable levels of XBP1s upon LPS stimulation as measured by Western blotting. Healthy mature and antibody producing B cells also have detectable sXBP1 protein.  However, I am not sure if the antibodies commercially available can be used for flow cytometry or not.

I cannot comment on other proteins.

yes, PBMC of healthy donors do express BCL-6 and can be detected by flow cytometry, when gated on all lymphocytes. However, expression is not very high (like GATA-3, Tbet) and mostly donor-dependent. No idea about B-cells.

Thank you for your helpful answers