1. Could we add a comparison feature directly from the search results (Dashboard view -> search -> highlight some experiments for comparison)?

Totally forgot about the global search feature, hmm I'm not sure the webapp is in the correct "state" for that, i.e. I think that the selection only works in "table view", which is the "all experiments" flat table

2. Could we add a filter on the project name in the "All Experiments" project?

You mean "filter by project" ?

Could we add the 

project

 for each of the search results? (see above picture where there's identical-named tasks, in different projects, but one cannot tell which is which)

I think you see it in the table itself? Do you mean on the card (when searching from the dashboard) ?