Many people, including locals who have more experience with foreign maids,
will tell you that luck plays a part. But it is a small part. There are so
many different things to consider.
First, you have to be clear in your mind what you can expect from a woman with less education than you, with less motivation than you, from a country less developed than yours. Because you have always managed at home without help, you are probably a pretty good housekeeper yourself. A maid who was a waitress or a dressmaker or a fishmonger before she stepped into your house is probably not half as efficient or competent as you are and therefore can probably accomplish only a fraction of what you yourself can achieve as a homemaker. Your maid is not a homemaker, but a paid worker.
Next, consider your values. Not all maids tell lies. And lying is not always seen as a bad thing where they come from. It is a way to avoid unpleasantness, a way to avoid confrontation or embarassment. In their environment they know when someone is lying to them, but they are prepared to let it go to avoid an ugly confrontation or embarassment.
Rudeshelen did not lie when she said that in the wet market sellers did not issue receipts; she was telling the truth as she understood it. But even though you told her to go to the Holland Road wet market, she preferred to go to the Farrer Road wet market she was more familiar with. You live right in between the two markets, so it made no difference to her which one she went to. She probably thought that it would be a matter of indifference to you. But by letting you believe that she had gone to Holland Road wet market, she was being deceitful, just as bad as lying. She would be embarassed to have been caught not following your instruction to a "T", so she pretended that she had gone to the wet market you named.
But this is not to excuse Rudehelen for her bad behaviour. She deserved to be fired for being rude and disrespectful. You probably realise now that the smarter maids who speak excellent English can be maddeningly cocky like Rudeshelen. That's why you were ready to hire someone whose command of English was only half that of Rudeshelen's because you expect her to be less cocky. In general, the smarter the maid, the more room you have to give her. If you think Rudeshelen is cocky, wait till you meet a Black-and-White amah!. A girl who is less experienced is more eager to please, more compliant, albeit also less competent.
If you are offended by lying, do not place your maid in such a position that her automatic reaction would be to lie. If Rudeshelen could not produce the receipts you could have let the matter pass and bring her to Holland Road wet market with you the next time you do your grocery shopping and show her that the sellers there do indeed issue receipts. Even if you say not a word, she would have got your message, "Don't try to con me again. I'm smart."
Since you do not like a maid who smokes, let a prospective maid know you will not accept a smoker. Tell her you had to let your former maid go for smoking. But do not threaten her with dismissal if you catch her smoking, because she will be afraid to work for you, even if she is not a smoker. For then you will appear "strict" to her (whatever that may mean) and she is afraid of a strict employer.
If the sink is dirty, do not ask her if she has washed it. You know the
answer already. If she says no, she is embarassed. She has reason to lie, to
save face. If she lies, you get mad. So to avoid embarassing her and getting
yourself all worked up, just simply tell her to wash the sink. And if she
says feebly that she has done it, tell her to do it again because it is
still dirty. You thus let her know, without embarassing her much, that you
have eyes to see.