It depends on the theme, while the theme shouldn't affect the available widgets, it's entirely possibly that it does - that is to say, the capability is there should the theme designer code it in.

I haven't tested any themes, so I can't confirm what you're reporting.  Maybe post on the theme page and ask if that behaviour is intentional.

The Cool Theme is a bad choice for testing which widgets you can add to dashboards and profile pages. The Cool theme is based on the Facebook theme. Both of these themes try to copy the Facebook look on Elgg sites and therefore remodel the profile pages and dashboard considerably including disabling some functionality you would have with the default Elgg theme (and most likely with 99% of all other themes, too). Additionally, all the Facebook themes known to me (original Facebook theme and its derivates) are very, very buggy. They always were buggy and they are also seem no longer maintained. Lack of maintenace is especially a bad thing for these theme plugins because they override a lot of core views (much more than themes do normally). The overriding (by buggy views) causes a lot of problems and most likely the number of problem is even increasing with each new Elgg core version as the Facebook themes do not react on any changes / bugfixes / security fixes that were made in Elgg core due to their lack of maintenance.

If you want to check widget compatibility with a theme enabled on your site I would suggest to try other themes - best would be themes that are still maintained or start with a simple theme that allows you to modify it according to your needs.

I see, thanks for your answers!

You are right, I found some problems evaluating the "goodness" of each plugin..

In this respect, I did also notice the plugins search page to be far from perfect: as far as I can see, it always sorts plugins by post date (probably "most recommended" would be a better choice...), and you can't sort them by other fields; more, I would add a column with the minimum elgg version supported (so no need to ask for an Elgg version selection in the plugins page...); and (this is an aesthetic suggestion...) I'd use a table layout to keep columns aligned... :-). More (and perhaps most important, given the big number of plugins / themes now available), I'd like a text search field in the plugins page...

I will for sure try a different theme, hoping it's widget compatibility is good... However, I find the fact a theme must be compatible with someting like widgets to be quite singular... I for sure must go deeper in Elgg knowledge...

Thanks again, everybody, and kudos for the good work!