Use Mana twice for the same spell by untapping?

Question

If your commander has an ability to untap card and you use it for untapping Mana, can you use it to pay for 6 Mana while there is only five in your pool.it was Estrid, the Masked untapping an enchanted land.

Answer 1

Yes, you can tap a land for mana again in the same turn if it becomes untapped.

When you can tap a land for mana, it always has some variation of "{T}: Add ..." as its ability, where {T} is the tap symbol. That is an activated ability. Activated abilities always follow the "cost: effect" pattern. Generally, you can activate an activated ability as often as you want, as long as you can pay its cost every time.

When you tap a land for mana, the mana it produces goes into the "mana pool", a temporary storage for your mana. Then, when you untap that land, you can pay the cost of its mana-generating ability again (i.e. tapping the land), and you will get another mana.

That means, if you have 5 lands, tap them for mana, and untap one of the lands, you can tap that land again to get 6 mana total.

602.1. Activated abilities have a cost and an effect. They are written as “[Cost]: [Effect.] [Activation instructions (if any).]”

602.1a The activation cost is everything before the colon (:). An ability’s activation cost must be paid by the player who is activating it.

106.4. When an effect instructs a player to add mana, that mana goes into a player’s mana pool. From there, it can be used to pay costs immediately, or it can stay in the player’s mana pool as unspent mana. Each player’s mana pool empties at the end of each step and phase, and the player is said to lose this mana. [..]

Answer 2

First we need to clarify what lands and mana are, because you're getting these mixed up.

The land cards you lay out in front of you are merely Lands. They are not mana or your mana pool. Lands are tapped to acquire mana, which then acts as a currency to pay for spells, as you'd be familiar with. The “mana pool” does not actually physically exist anywhere on the table, it's purely conceptual as a way to think about your mana.^(note)

This means when you tap a Forest you get {G} (one green mana), and you spend that {G} to cast a spell. Other cards such as Llanowar Elves can also give you mana, although they are not lands. Some cards such as Cascading Cataracts can give you more than one mana.

You can absolutely untap a land and then tap it again to obtain more mana. In fact this is why cards like Arbor Elf or Blossom Dryad exist: they let you untap a land so that you can tap it again for more mana.

If you had five basic lands (let's say 2 plains, 2 islands, 1 forest) you can tap each of them for mana. Then, yes, you can use Estrid's ability to untap the one that's enchanted, and tap that again for one more mana. You would then have six mana.

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^{Note: The “mana pool” concept no longer gets referenced on new cards, as of Dominaria. Cards printed in and after that set only reference adding mana, but without referring to a mana pool when they do so.}

Answer 3

YES, you can.

A land really has the implicit text "Tap: Add [land_specific mana] to your mana pool". So, the cost to activate this mana-producing ability is to TAP the land.

Other mana sources require tapping (for example, Llanowar Elves, or Mox artifacts), others require sacrificing (for example, the "Black Lotus" from the alpha/beta edition), and so on. As long as you can meet the cost, you may activate the ability.

So, if you activate your lands to add the mana to your pool, THEN activate the loyalty ability from the planeswalker to untap all the enchanted permanents you control, and some of these enchanted permanents happen to be lands, sure, you can tap them again to add their mana to your pool once more.

However, you need to keep in mind that you may only activate a Planeswalker's Loyalty ability as a Sorcery (and only ONE such ability par turn and per planeswalker. Also, if the number on the ability is positive, you gain that much loyalty on that planeswalker, but if the number is negative, you need to have enough loyalty on the planeswalker to "pay" for the ability.)

This means that you CANNOT use the planeswalker's loyalty ability WHILE casting your spell, and getting the mana. That's not a mana-providing ability, it cannot be played as a fast effect, only as a sorcery. You need to do so BEFORE you cast your spell.