1-Do I qualify for a discount at my age of sixty years?
Is '1' correct?
2-I have decided to sell my house in Los Angeles.
Does '2' imply that I have more than one house (one of which is in Los Angeles)?
3-My brother in Italy called me up.
Does '3' imply that I have more than one brother?
1 is unnatural. "I'm 60. Do I qualify for a discount?", "Will I get a discount because I'm 60?", "Do I get a discount for being 60?"
2 is ambiguous. It could be your only house and you're just giving extra information about its location. You could have another house that isn't in LA.
3 is ambiguous for the same reason. You might just want to throw in the fact that your brother lives in Italy or you might have other brothers elsewhere.
To avoid ambiguity you'd have to say "I have decided to sell my house in LA but keep my other one/my others", and "My brother, who lives in Italy, called me". To be honest, with the "brother" one, it could still be possible that you have other brothers but it is less likely. Most people don't refer to "One of my brothers" unless it's absolutely necessary.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.