Yes, local accounts are those that exist - are/have logged in - on the same console, whether created there or elsewhere.
The Playstation Plus subscription is tied to the SEN account, but that account can specify a single PS4 console as its primary PS4, which enables other (non-PS+) accounts to access everything on the console.
So any account using that console (the one specified as the primary by at least 1 PS+ subsriber) can enjoy the benefits of PS+, when using that console. That includes multiplayer.
I assume though that multiplayer is not available to local accounts if you are online and playing multiplayer on someone else's console. That part isn't exactly clear. But your (non-PS+)family members / housemates could definitely play multiplayer on your console with only your PS+ subscription when you're not using it.
This FAQ on playstation.com is fairly detailed:
PlayStation 4
You can activate one PS4™ on your Sony Entertainment Network account
(this is known as your Primary PS4) and temporarily activate a second
PS4 on your account.
PlayStation Plus benefits available to other non-subscribing users on your Primary PS4:
- Online multiplayer (subject to any parental control settings on sub-accounts)
- Play downloaded games purchased with PlayStation Plus discount
- Play downloaded IGC games
PlayStation Plus benefits not available to other users on your Primary PS4:
- Purchasing PlayStation Plus discounted products from PlayStation Store
- Online game save storage
- Auto patch download
- PlayStation Plus exclusive early access to game trials
PlayStation Plus benefits available to you on a non-subscribing friend’s PS4:
- All of your PlayStation Plus membership benefits are available to you when you use a friend’s PS4.
PlayStation Plus benefits available to your non-subscribing friend when you use their PS4:
- Play downloaded games purchased with PlayStation Plus discount
- Play downloaded IGC games
PlayStation Plus benefits not available to your non-subscribing friend when you use their PS4:
- Online multiplayer (subject to any parental control settings on sub accounts)
- Purchasing PlayStation Plus discounted products from PlayStation Store
- Online game save storage
- Auto patch download
- PlayStation Plus exclusive early access to game trials
When you sign into your Sony Entertainment Network on a friend’s PS4
the system is temporarily activated on your account. Please ensure
that you correctly sign-out of “PSN” on your friend’s system to keep
your account secure.
If your “PSN” account is inactive on your friend’s PS4, the system
will be deactivated automatically from your account and your friend
will lose access to any of your downloaded content. This content can
be deleted from their system hard drive by going to Image (Settings) >
System Storage Management > Applications. Next, highlight the game to
delete and press Options > Image (X button).
Source: http://faq.en.playstation.com/app/answers/detail/a_id/5030
Your data is tied to your PlayStation account, not the physical hardware. Otherwise, a fried motherboard could cost years of time spent.
You need to follow the same directions for upgrading the hard drive in your PS4, except you will be replacing the whole console, not just the hard drive:
Upgrade PS4 HDD
You can sync your save data on the cloud if you have a PlayStation Plus account (the one you pay money for each month).
You can sync your save data locally using a USB stick.
You will need to reinstall your games on the new console to include downloading those massive updates again unless you back up to a larger USB storage medium, such as a USB hard drive. Unless you have one laying around, that is a lot of money to spend when you can just have the new console update overnight while you sleep.
Any DLC (e.g. The Taken King) or digitally-purchased content such as buying a game or other app in the PlayStation store as opposed to the physical disc is tied to your account. Once you set up the new console with your existing account and you are connected to the Internet you can go to "library" and select it to download it.
I upgraded my PS4's hard drive very recently and have been through the backup/restore process. It took a while to reinstall and update everything, but the process was very easy, and none of my save games were missing or broken. I have all of my paid content available, including games I bought digitally. The process is not very intimidating and they make it easy even for nontechnical people.
Best Answer
If by Gift Card you are referring to Prepaid cards to top up your wallet, then unless the other accounts can buy though another account, the answer is generally no.
Prepaid cards add funds to a PlayStation Network Account which is actually independent from any console as you can access your PlayStation Network account though the browser and buy stuff that way.
When you say,
I am assuming that you are referring to the associated PlayStation Network Accounts which would have their own Wallets with their own funds and generally are independent from each other.
An exception to this is using Family Accounts where the Child Family Member Accounts can spend money from the Family Manager account.
However, once these accounts are detected to have turned 18, they graduate to Adult Family Members and are then unable to spend funds from the wallet of the Family Manager. This trade off is probably due to the fact that Child Family Member Accounts cannot add funds to their wallets whereas Adult Family Member accounts can and can also leave the Family Account (although they lose access to shared content).
If however, this gift card is part of a free game giveaway, then even if an account isn't part of the Family, it can still access the game on any that it shares with that account.