Are ecuмenical councils completely infallible? No.
The solemn definitions of a council approved by the pope are infallible.
Yes.
Ecuмenical councils are USUALLY good because they are USUALLY part of the universal magisterium, since the purpose of councils is to clarify, re-teach, and educate catholics on those topics which are under attack through error or heresy. When all the bishops, in union with the pope, teach on faith and morals, such teachings are infallible with a lowercase 'i', as part of the magisterium, because the bishops are teaching 'what has always been taught'.
Vatican 2 didn't teach anything dogmatically, or define anything new (unfortunately, there were some good Cardinals who wanted to do so, but they were outvoted). Vatican 2's evil genius was in concentrating on the "pastoral" aspects of the Faith, which means it attempted to subvert Church teachings by altering how the Faith is "applied" at a church level.