Generally:

Best bet is to pay the rent. The landlord may be strapped for cash and waiting on your income to make the repairs you want. This way you can also say that you are upholding your end of the contract if it comes time for court. Certain parts of the law regarding breaking your lease requires this (see link).

It is best to avoid court if at all possible, but start keeping written records of maintenance requests. Some lease contracts (the standard one use by the Texas Apartment Association for example) have clauses that maintenance requests MUST be in writing. In practice good managers don’t enforce this.

Remember that unless it is something that actively endangers you, like a gas leak, it generally isn’t considered an emergency.

The requirement that you be home when repairs are made is unusual. It is likely he is trying to cover himself legally. They should be able to repair without you present, BUT I am not sure if that is something that can be enforced.

I can make this answer longer, but there is an excellent link that spells out what you need to do step by step. Read it so you can see what your rights are under the law.

I wouldn’t sweat it if you need to break the lease. Unless the rental market is very tight, you probably wont have much trouble. Doesn’t sound like its’ very competitive if the landlord allowed you to move in without paying rent.