Learn English – Difference between “and” , “or”

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]

The government has spent a great deal of money attempting to help the region.

is the best sounding choice to me. Probably context has a lot to do with it.
For example, big is better here:

I don't really care about failing the exam. It's no big deal, really.

And the last example (including a different grammar correction):

It was time for her to make the big decision. Should she agree to marry him?

or

It was time for her to make the big decision should she agree to marry him.

But in another context:

You made a lot of money. That was a great decision.

In these kinds of examples, great refers to something very positive or beneficial (or very negative or disasterous), while "big" has more to do with the importance of something (as in the marriage decision).