Should the federal government be able to force state governments to change their education system, given that education is mostly a right reserved to the states under the 10th amendment ?

The Federal government is not allowed to force schools to change the ways they teacher their own students. However when Common Core was released by the Obama Administration, states and schools had little choice in the matter, because if they refused they would not received their funding.

whose power in the senate is equal to the power of the speaker of the house?

the answer to your question is:

strong-mayor system