First issue: Moodle was supposed to handle the incompatible block case automatically, so you should not have got the first error. It would be very helpful if you could tell me exactly what version of 1.5+ you were installing, and what version you were upgrading from. And also post the offending block here, if you can.
Second issue: the recent activity block... this has happened again. Recent activity for some reason dies without warning, and the rest of the page (including the "add blocks" block and the footer) does not get displayed. Are there any fatal errors in the log? Also, some people have found that removing non-standard modules (not blocks) they have causes recent activity to behave again.
If you try this and after removing a module recent activity starts working again, please remember to post some information (name, version) about that module here.
Jon