By joining the EU, the Swiss would agree to transfer legislative competence in certain areas to the European Parliament (in conjunction with the Council of the European Union). These areas are set out in Title I of the Treaty on the Functioning of the European Union. Anything not on this list remains within the sole competence of the member state, to be decided upon in whatever (democratic) way that state chooses.
As such, there is no reason why the Swiss could not continue to have popular votes on their constitution and national laws - except for laws in areas of exclusive union competence, and laws in shared union competence that contradict EU law.
To make this a little clearer, let's look at your provided examples:
- The vote on federal taxation would stand, because taxation is outside union competence.
- The vote about the Swiss monetary system would stand, because the EU has monetary competency only for member states that have chosen to adopt the Euro.
- The initiative about the precedence of the Swiss law over international law is an interesting case. If adopted, it would have required the Swiss government to renegotiate any international treaty contradicting Swiss law, or leave the treaty if such negotiation was not possible. If the conflict was with passed EU law, renegotiation would have been procedurally difficult, and the Swiss government would likely have been required to leave the EU as a result.
- The initiative about financial incentives for farmers whose cows have horns would most likely stand, since agriculture is an area of shared union competency, and I can't imagine the EU passing a directive that would forbid additional funding for cow horns.
As you can see, none of these votes would have been prevented by EU law, and all would have been binding.
In addition, the Swiss might be able to make their participation in the EU lawmaking process more direct than usual by passing a (national) law that requires their representatives in the Council of the European Union to vote in accordance with a previously held popular vote.
In summary, joining the EU would mean that policy in some areas could no longer be decided by the Swiss alone, but in all other areas, Switzerland would retain full sovereignty, and the Swiss would be free to vote as directly as they please.