Learn English – What are the differences between “I’m broke” and “I don’t have money”

Firstly, I think your second example should be have saved, rather than have save.

To save up pretty much always means deliberately putting money aside for something. There will be a purpose, and a defined saving period: you choose when to start saving, and you finish when you (hopefully) reach a certain amount, and/or reach a deadline. The 'up' implies working towards something, even if it is not specified in the sentence.

To save can imply that you are putting money aside, gathering/gaining money, or not spending money. There may be a specific purpose, target amount, deadline, but there may not. It can be deliberate or not.

A simple rule: (in my experience of British English), if there is no target/purpose, you should say 'save', not 'save up'. If there is a target/purpose, 'save up' is more natural (although you can say 'save').

Examples:

• You get a 33% discount at a shop. You look at the receipt to see how much money you have saved [=not had to pay].
• You put 10% of your wages into a separate account each month. You look at the balance to see how much money you have saved [=accrued, no obvious purpose].
• You put 10% of your wages into a separate account each month so you can buy a house one day. You look at the balance to see how much you have saved up [=accrued, specific purpose
• You stopped buying takeaway coffee two years ago. You do a quick calculation to see how much you have saved [=not spent]. It's a lot!
• You are going on holiday next year and it's going to be expensive, so you are saving up [=deliberately putting money aside] for it.
• Your friend asks if you want to go for dinner. You would love to, but you say no, because you're saving up [=deliberately putting money aside] for a new car.
• Your friend asks if you want to go for a drink. You would love to, but you say no, because you're trying to save money [=generally trying to spend less money].
• You are hoping to have a baby in a few years, so you are saving up [=deliberately putting money aside because you know you will need it, even if you don't know exactly how much it will cost, or what you will buy]

1: You wanted to do it means that at some point in the past you were willing to do it

3: You would do it means it isn't always something you are willing to do but you may do it if...

EDIT:

Want suggests desire, it implies that you are happy to do something, if you want something you'll take measures to get it (trade, buy, steal...)

• I want a pony, I'll go out and get one if I can.
• I wanted to go to London but something stopped me.
• I would want to go to Spain but I can't afford to.

Willing suggests that you will do something, but you might need to be persuaded or paid. It in no way means want.

• I am willing to look after a pony, but I'm not going to try to get one.
• I was willing to go to London but I had no reason to go.
• I would be willing to go to Spain with you if you want to go, otherwise I would not go.