1) The yard is .25 acres. And has 2 big mature trees in the back and 2 medium trees in the front. Are the renters responsible for caring for the yard or do we hire someone to care for it twice a week and roll the cost into the rental?
Yes. Or you mow it yourself. In other words, it's how you want to offer it and whether the renter wants it that way.
2). Our current stove is working fine, but one burner is not. Only 3 out of 4 burner is working. Do we have to replace The stove completely?
Yes or no. Have you tried getting it repaired?
Unless you specifically advertise it has a stove with only 3 of 4 burners working and that's how it's going to stay or you don't provide a stove at all, then yes, you are expected to provide a working stove. Local laws might require the stove to be fully working regardless.
Frankly, if you provide a stove and it doesn't work properly, you're going to limit your potential renter pool. And skew it to the worst of the worst, too. Frankly, I wouldn't rent from a landlord who was too cheap to fix the stove unless I had no other choice. And if I had no other choice, it's probably because I'm broke and desperate, neither of which are good renter material.
3). The flooring in the kitchen needs to be replace. Fortunately, we have family members that can assist us. What kind of flooring you recommend for rentals that are long lasting and water proof?
Nothing is water proof, you can only get water resitant. Water will find it's own way given time. :(
Linoleum is cheap and easy to install. Tile is another option depending on the subflooring.
Partly it depends on the type of house and the neighborhood. Sometimes you need to go more upscale.
What liabilities come into mind that we should be careful and aware of?
Ignorance.
Ignorance on the financials of how to calculate whether you're making a profit.
Ignorance on landlording laws in your state and locality.
Have you read some (hopefully many) of the resources listed on the RE sub-forum?