Spagoh,
From what you told me, in your gal's case might be she hasn't fully understand the concepts yet. That is for Math.
For English, don't need to worry about your gal not knowing how to read a storybook by herself. She's only 6 this yr. Alot of P1s still can't read a book by themselves yet. So no need to stress your gal so much in this. Just let her remember the simple words like is, are, was, were, we, you etc... You can buy cardboards and cut them into tiny pieces and do a flash card game with her.
Another thing to note for her English language development now is her phonics. Make sure she knows the sound of each letter and that will help her in making up words easier when it comes to reading and spellings.
When you give her rewards, you state your terms clearly and firmly. Give her a time limit for eg, "If you are able to find 10 qns by 10.30am, I'll bring you to XXX place. But I do not want to hear you talking now. Do your work quietly." and leave her alone to do, make sure all distractions are off. And by that time you come in at 10.30am, if she hasn't finish her work. Tell her you'll not bring her anymore and stick to your word regardless of her cryings and temper.
That should cultivate discipline in her. Many of the times as parents, the kids knows our limits. Many parents have this weakness, esp when their kids starting showing temper, they give in cos they feel for their child. Thats why most children behave better in schools than home, cos the teachers set rules and will stick by it, while many children knows their own parents are flexible with the rules. But once you let her know you mean what you said, eventually she'll learn and she'll take your words seriously.
I know perhaps you think saying is easier than done but I've seen parents done it and their children know their parents mean business. This will also teach your child to obey rules and take responsibility for their own actions when they grow up.
Another I observe from what you told me is that she might lack alot of confidence in herself. Why I said that is because from what you told me, she is very scared of making mistakes thats why she's very dependent on you to spoonfeed her with answers.
You might want to encourage her to try on her own and ignore her pesterings. Tell her to try doing it herself. When she's done and even if it's a mistake, let her know that it is ok to make mistakes. And still give her the reward. And when giving her the reward, tell her you are rewarding her for trying and completing her work on time.
Don't give yourself and your gal too much pressure. Our times we weren't put through so much presuure but we still survive rite?
Every child only have 1 childhood, let them have fond memories of their childhood rather than it's all about education.
This is something I really hate abt Singapore education system. Becos we focus too heavily on academic performance, our children are missing out alot in life.