Can I Refuse To Let Landlord Do Construction In My Apartment?

There mat be reasons why he would need to carry out work in the apartment. As he is the owner of the property, he is entitled to carry out work, perhaps for safety issue and if you prevent him from doing so, should anything happens, then you can't sue him.

He should however, give you notice first,let you what exactly he is going to do, why and when, so it would disturb you, as it might cause inconvenience. Depending on the type of work, if its unhealthy for you to stay in the apartment whilst the work is in progress and depending how long the work will taken, then its his responsibility to make sure it is safe for you to stay whilst the work is being done.

Yes you can refuse the repairs but if its a health code violation and you plan on staying there for a while might want the bastard to fix it.

Yes, but sometime repair necessary. So my advice is to keep construction in your apartment this is for your benefit.