Learn English – Difference between “Thanks God” and “Thank God”

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]

However you look at this question it's not easy to answer

Whereas ignoring it is the easy option

However, neither will keep me awake at night

I'd always use "whereas" as the second part of a comparison. "however" could also be used in this way. Often "however" would have a comma after it when used as the second part of a comparison.

I take "however" as something like "how ever you take the meaning of this" .
OTOH "whereas" is something like "in contrast to the previous opinion"