what loads working or ultimate should be taken in foundation design

In answer to your first query only, I would suggest that foundation design is not really any different from the rest of structural design in regard to the use of 'ultimate' or 'working' loads.

Whether we are designing steel or concrete structures, BOTH types of load need to be considered for most structures.

For load capacity, many (most ?) design codes now specify that you calculate structural strength under ultimate loads and provide some reserve against total collapse. But that is not all that they require.

Most codes also specify particular limits that apply under 'serviceability' or 'working' conditions. These may include limits on deflections, crack widths in reinforced concrete (especially for water retaining structures), perhaps zero tension stress in prestressed concrete.

When it comes to the foundations, you have a similar situation.

The reinforced concrete design can be done with ultimate loads, but the permissible bearing pressure can often depend on the maximum acceptable settlement under actual loading, and therefore common practice is to specify it as a 'working' limit.

Taking the issue from a Geotechnical view point, The actual foundation and supporting soils tend to 'feel' a fairly light structure. When I have jacked/repaired structures, they are usually 'light', compared to calculated loads. Dead loads are usually overestimated as a whole. It must be recognized that ndividual beams, columns and slabs may experience localized heavier dead loads. The same reasoning is even more apparent with live loads, except for some types of structures ( i.e. Rigid-framed steel structures experiencing wind loads).

As far as the sizing footings, I have seen quite a few criteria, depending on local practices, size of structure/loads and the soil conditions. Residential and light commercial being a 'horse of a different Merry-go-Round' as compared to heavy, multi-story structures.

The correct methodology would be to perform settlement analysis for diffrent loadings and try to minimize differential settlement. As a start for determining loading combinations I suggest the following.

When dealing with light (5 to 20 k/pad) to medium weight (20 to 50 k/pad) structures, on compressible soils (.8 to 3 k/ft), I typically see DL + 1/2 LL for up to 3 stories and DL + 1/3 to 1/4 LL for more than 3 stories. I have seen and used similar criteria for heavier structures on somewhat stronger soils (3 to 5 k/ft).

When dealing with expansive soils, I typically use dead load to confirm the minimum load condition is met (and I try to stay 20% to 50% above the minimum required, if possible). I check DL + LL for the Maximum Allowable, possibly allowing for a 10% to 20% overload, depending on how good or bad I think the information is.

Looking back on this, it reads like a hydrologist giving his anticipated flows. My Father always said that Hydraulics and Geotechnics is half art. He should have known, He was both.

I hope this helps.