No, they couldn't.
Yes they could - a constitional ammendment trumps any other part of the constitution.
Don't be silly Sink, it ain't likely, but they could, by ammending the constitution, and as long as they got the states to ratify it, it would ne constitutional. In fact the states could do it without the congress by calling for a Constitutinal convention.
Again it is not likely, but not impossible.
On the other hand The President has no such power under the constitution, his only power to abolish the congress, would be by military coup.