What types of rules are there regarding e.g. attendance,

Contractual: Attendance requirements are defined by employment contracts.

affiliation in publications,

List both, since you are employed by both. Perhaps order affiliations by who paid for the work, or include an acknowledgement to the institute that funded the research.

teaching,

Contractual

PhD supervision,

Your institutes will likely have expectations, either explicit or implicit. You'll have your own expectations.

committee membership,

Likely institutional expectations, e.g., you must serve on at least one committee.

access to funding,

Apply using the most favourable institution

lecturing responsibilities,

I don't understand this point.

and salary

You can negotiate with each institute.

I'd appreciate pointers to corresponding policies or regulations.

Institutionally specific.

What types of rules are there regarding e.g. attendance,

Contractual: Attendance requirements are defined by employment contracts.

affiliation in publications,

List both, since you are employed by both. Perhaps order affiliations by who paid for the work, or include an acknowledgement to the institute that funded the research.

teaching,

Contractual

PhD supervision,

Your institutes will likely have expectations, either explicit or implicit. You'll have your own expectations.

committee membership,

Likely institutional expectations, e.g., you must serve on at least one committee.

access to funding,

Apply using the most favourable institution

lecturing responsibilities,

I don't understand this point.

and salary

You can negotiate with each institute.

I'd appreciate pointers to corresponding policies or regulations.

Institution specific.